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    <title>Fundamenta Informaticae - Latest Publications</title>
    <description>Latest articles</description>
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    <pubDate>Fri, 03 Apr 2026 20:30:22 +0000</pubDate>
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    <author>Fundamenta Informaticae</author>
    <dc:creator>Fundamenta Informaticae</dc:creator>
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    <item>
      <title>An Elementary Proof of the FMP for Kleene Algebra</title>
      <description><![CDATA[Kleene Algebra (KA) is a useful tool for proving that two programs are equivalent. Because KA's equational theory is decidable, it integrates well with interactive theorem provers. This raises the question: which equations can we (not) prove using the laws of KA? Moreover, which models of KA are complete, in the sense that they satisfy exactly the provable equations? Kozen (1994) answered these questions by characterizing KA in terms of its language model. Concretely, equivalences provable in KA are exactly those that hold for regular expressions. Pratt (1980) observed that KA is complete w.r.t. relational models, i.e., that its provable equations are those that hold for any relational interpretation. A less known result due to Palka (2005) says that finite models are complete for KA, i.e., that provable equivalences coincide with equations satisfied by all finite KAs. Phrased contrapositively, the latter is a finite model property (FMP): any unprovable equation is falsified by a finite KA. Both results can be argued using Kozen's theorem, but the implication is mutual: given that KA is complete w.r.t. finite (resp. relational) models, Palka's (resp. Pratt's) arguments show that it is complete w.r.t. the language model. We embark on a study of the different complete models of KA, and the connections between them. This yields a novel result subsuming those of Palka and Pratt, namely that KA is complete w.r.t. finite relational models. Next, we put an algebraic spin on Palka's techniques, which yield a new elementary proof of the finite model property, and by extension, of Kozen's and Pratt's theorems. In contrast with earlier approaches, this proof relies not on minimality or bisimilarity of automata, but rather on representing the regular expressions involved in terms of transformation automata.]]></description>
      <pubDate>Fri, 06 Feb 2026 09:21:39 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12445</link>
      <guid>https://doi.org/10.46298/fi.12445</guid>
      <author>Kappé, Tobias</author>
      <dc:creator>Kappé, Tobias</dc:creator>
      <content:encoded><![CDATA[Kleene Algebra (KA) is a useful tool for proving that two programs are equivalent. Because KA's equational theory is decidable, it integrates well with interactive theorem provers. This raises the question: which equations can we (not) prove using the laws of KA? Moreover, which models of KA are complete, in the sense that they satisfy exactly the provable equations? Kozen (1994) answered these questions by characterizing KA in terms of its language model. Concretely, equivalences provable in KA are exactly those that hold for regular expressions. Pratt (1980) observed that KA is complete w.r.t. relational models, i.e., that its provable equations are those that hold for any relational interpretation. A less known result due to Palka (2005) says that finite models are complete for KA, i.e., that provable equivalences coincide with equations satisfied by all finite KAs. Phrased contrapositively, the latter is a finite model property (FMP): any unprovable equation is falsified by a finite KA. Both results can be argued using Kozen's theorem, but the implication is mutual: given that KA is complete w.r.t. finite (resp. relational) models, Palka's (resp. Pratt's) arguments show that it is complete w.r.t. the language model. We embark on a study of the different complete models of KA, and the connections between them. This yields a novel result subsuming those of Palka and Pratt, namely that KA is complete w.r.t. finite relational models. Next, we put an algebraic spin on Palka's techniques, which yield a new elementary proof of the finite model property, and by extension, of Kozen's and Pratt's theorems. In contrast with earlier approaches, this proof relies not on minimality or bisimilarity of automata, but rather on representing the regular expressions involved in terms of transformation automata.]]></content:encoded>
      <slash:comments>0</slash:comments>
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    <item>
      <title>Cardinality and Representation of Stone Relation Algebras</title>
      <description><![CDATA[Previous work has axiomatised the cardinality operation in relation algebras, which counts the number of edges of an unweighted graph. We generalise the cardinality axioms to Stone relation algebras, which model weighted graphs, and study the relationships between various axioms for cardinality. This results in simpler cardinality axioms also for relation algebras. We give sufficient conditions for the representability of Stone relation algebras and for Stone relation algebras to be relation algebras.]]></description>
      <pubDate>Fri, 06 Feb 2026 09:21:11 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12347</link>
      <guid>https://doi.org/10.46298/fi.12347</guid>
      <author>Furusawa, Hitoshi</author>
      <author>Guttmann, Walter</author>
      <dc:creator>Furusawa, Hitoshi</dc:creator>
      <dc:creator>Guttmann, Walter</dc:creator>
      <content:encoded><![CDATA[Previous work has axiomatised the cardinality operation in relation algebras, which counts the number of edges of an unweighted graph. We generalise the cardinality axioms to Stone relation algebras, which model weighted graphs, and study the relationships between various axioms for cardinality. This results in simpler cardinality axioms also for relation algebras. We give sufficient conditions for the representability of Stone relation algebras and for Stone relation algebras to be relation algebras.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Normal Forms for Elements of ${}^*$-Continuous Kleene Algebras Representing the Context-Free Languages</title>
      <description><![CDATA[Within the tensor product $K \mathop{\otimes_{\cal R}} C_2'$ of any ${}^*$-continuous Kleene algebra $K$ with the polycyclic ${}^*$-continuous Kleene algebra $C_2'$ over two bracket pairs there is a copy of the fixed-point closure of $K$: the centralizer of $C_2'$ in $K \mathop{\otimes_{\cal R}} C_2'$. Using an automata-theoretic representation of elements of $K\mathop{\otimes_{\cal R}} C_2'$ à la Kleene, with the aid of normal form theorems that restrict the occurrences of brackets on paths through the automata, we develop a foundation for a calculus of context-free expressions without variable binders. We also give some results on the bra-ket ${}^*$-continuous Kleene algebra $C_2$, motivate the ``completeness equation'' that distinguishes $C_2$ from $C_2'$, and show that $C_2'$ already validates a relativized form of this equation.]]></description>
      <pubDate>Wed, 14 Jan 2026 10:44:50 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12479</link>
      <guid>https://doi.org/10.46298/fi.12479</guid>
      <author>Hopkins, Mark</author>
      <author>Leiß, Hans</author>
      <dc:creator>Hopkins, Mark</dc:creator>
      <dc:creator>Leiß, Hans</dc:creator>
      <content:encoded><![CDATA[Within the tensor product $K \mathop{\otimes_{\cal R}} C_2'$ of any ${}^*$-continuous Kleene algebra $K$ with the polycyclic ${}^*$-continuous Kleene algebra $C_2'$ over two bracket pairs there is a copy of the fixed-point closure of $K$: the centralizer of $C_2'$ in $K \mathop{\otimes_{\cal R}} C_2'$. Using an automata-theoretic representation of elements of $K\mathop{\otimes_{\cal R}} C_2'$ à la Kleene, with the aid of normal form theorems that restrict the occurrences of brackets on paths through the automata, we develop a foundation for a calculus of context-free expressions without variable binders. We also give some results on the bra-ket ${}^*$-continuous Kleene algebra $C_2$, motivate the ``completeness equation'' that distinguishes $C_2$ from $C_2'$, and show that $C_2'$ already validates a relativized form of this equation.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Relational Algebraic Approach to the Real Numbers: The Least-Upper-Bound Property</title>
      <description><![CDATA[In this paper we continue the investigation of a real number object, i.e., an object representing the real numbers, in categories of relations. Our axiomatization is based on a relation algebraic version of Tarski's axioms of the real numbers. It was already shown that the addition of such an object forms a dense, linear ordered abelian group. In the current paper we will focus on the least-upper-bound property of such an object.]]></description>
      <pubDate>Sun, 11 Jan 2026 21:43:23 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12364</link>
      <guid>https://doi.org/10.46298/fi.12364</guid>
      <author>Winter, Michael</author>
      <dc:creator>Winter, Michael</dc:creator>
      <content:encoded><![CDATA[In this paper we continue the investigation of a real number object, i.e., an object representing the real numbers, in categories of relations. Our axiomatization is based on a relation algebraic version of Tarski's axioms of the real numbers. It was already shown that the addition of such an object forms a dense, linear ordered abelian group. In the current paper we will focus on the least-upper-bound property of such an object.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Representing Sugihara monoids via weakening relations</title>
      <description><![CDATA[We show that all Sugihara monoids can be represented as algebras of binary relations, with the monoid operation given by relational composition. Moreover, the binary relations are weakening relations. The first step is to obtain an explicit relational representation of all finite odd Sugihara chains. Our construction mimics that of Maddux (2010), where a relational representation of the finite even Sugihara chains is given. We define the class of representable Sugihara monoids as those which can be represented as reducts of distributive involutive FL-algebras of binary relations. We then show that the class of representable distributive involutive FL-algebras is closed under ultraproducts. This fact is used to demonstrate that the two infinite Sugihara monoids that generate the quasivariety are also representable. From this it follows that all Sugihara monoids are representable.]]></description>
      <pubDate>Sun, 11 Jan 2026 21:42:32 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12451</link>
      <guid>https://doi.org/10.46298/fi.12451</guid>
      <author>Craig, Andrew</author>
      <author>Robinson, Claudette</author>
      <dc:creator>Craig, Andrew</dc:creator>
      <dc:creator>Robinson, Claudette</dc:creator>
      <content:encoded><![CDATA[We show that all Sugihara monoids can be represented as algebras of binary relations, with the monoid operation given by relational composition. Moreover, the binary relations are weakening relations. The first step is to obtain an explicit relational representation of all finite odd Sugihara chains. Our construction mimics that of Maddux (2010), where a relational representation of the finite even Sugihara chains is given. We define the class of representable Sugihara monoids as those which can be represented as reducts of distributive involutive FL-algebras of binary relations. We then show that the class of representable distributive involutive FL-algebras is closed under ultraproducts. This fact is used to demonstrate that the two infinite Sugihara monoids that generate the quasivariety are also representable. From this it follows that all Sugihara monoids are representable.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Unidirectional Key Update in Updatable Encryption, Revisited</title>
      <description><![CDATA[In this paper we construct a new efficient updatable encryption (UE) scheme based on FrodoPKE learning with errors key encapsulation. We analyse the security of the proposed scheme in the backward-leak uni-directional setting within the rand-ind-eu-cpa model. Since the underlying computationally hard problem here is LWE, the scheme is secure against both classical and quantum attacks.]]></description>
      <pubDate>Sun, 11 Jan 2026 21:39:26 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.14425</link>
      <guid>https://doi.org/10.46298/fi.14425</guid>
      <author>Jurkiewicz, M.</author>
      <author>Prabucka, K.</author>
      <dc:creator>Jurkiewicz, M.</dc:creator>
      <dc:creator>Prabucka, K.</dc:creator>
      <content:encoded><![CDATA[In this paper we construct a new efficient updatable encryption (UE) scheme based on FrodoPKE learning with errors key encapsulation. We analyse the security of the proposed scheme in the backward-leak uni-directional setting within the rand-ind-eu-cpa model. Since the underlying computationally hard problem here is LWE, the scheme is secure against both classical and quantum attacks.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
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      <title>Privacy for Quantum Annealing. Attack on Spin Reversal Transformations in the case of cryptanalysis</title>
      <description><![CDATA[This paper demonstrates that applying spin reversal transformations (SRT), commonly known as a sufficient method for privacy enhancement in problems solved using quantum annealing, does not guarantee privacy for all possible cases. We show how to recover the original problem from the Ising problem obtained using SRT when the resulting problem in Ising form represents the algebraic attack on the $E_0$ stream cipher. A small example illustrates how to retrieve the original problem from that transformed by SRT. Moreover, we show that our method is efficient also for full-scale problems.]]></description>
      <pubDate>Sun, 11 Jan 2026 21:38:45 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.14346</link>
      <guid>https://doi.org/10.46298/fi.14346</guid>
      <author>Leśniak, Mateusz</author>
      <author>Wroński, Michał</author>
      <dc:creator>Leśniak, Mateusz</dc:creator>
      <dc:creator>Wroński, Michał</dc:creator>
      <content:encoded><![CDATA[This paper demonstrates that applying spin reversal transformations (SRT), commonly known as a sufficient method for privacy enhancement in problems solved using quantum annealing, does not guarantee privacy for all possible cases. We show how to recover the original problem from the Ising problem obtained using SRT when the resulting problem in Ising form represents the algebraic attack on the $E_0$ stream cipher. A small example illustrates how to retrieve the original problem from that transformed by SRT. Moreover, we show that our method is efficient also for full-scale problems.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>MNT Elliptic Curves with Non-Prime Order</title>
      <description><![CDATA[Miyaji, Nakabayashi, and Takano proposed the algorithm for the construction of prime order pairing-friendly elliptic curves with embedding degrees $k=3,4,6$. We present a method for generating generalized MNT curves. The order of such pairing-friendly curves is the product of two prime numbers.]]></description>
      <pubDate>Wed, 31 Dec 2025 23:00:00 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.14373</link>
      <guid>https://doi.org/10.46298/fi.14373</guid>
      <author>Grześkowiak, Maciej</author>
      <dc:creator>Grześkowiak, Maciej</dc:creator>
      <content:encoded><![CDATA[Miyaji, Nakabayashi, and Takano proposed the algorithm for the construction of prime order pairing-friendly elliptic curves with embedding degrees $k=3,4,6$. We present a method for generating generalized MNT curves. The order of such pairing-friendly curves is the product of two prime numbers.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Ciphertext Malleability in Lattice-Based KEMs as a Countermeasure to Side Channel Analysis</title>
      <description><![CDATA[Due to developments in quantum computing, classical asymmetric cryptography is at risk of being breached. Consequently, new Post-Quantum Cryptography (PQC) primitives using lattices are studied. Another point of scrutiny is the resilience of these new primitives to Side Channel Analysis (SCA), where an attacker can study physical leakages. In this work we discuss a SCA vulnerability due to the ciphertext malleability of some PQC primitives exposed by a work from Ravi et al. We propose a novel countermeasure to this vulnerability exploiting the same ciphertext malleability and discuss its practical application to several PQC primitives. We also extend the seminal work of Ravi et al. by detailing their attack on the different security levels of a post-quantum Key Encapsulation Mechanism (KEM), namely FrodoKEM. We also provide a generalisation of their attack to different parameters which could be used in future similar primitives.]]></description>
      <pubDate>Tue, 30 Dec 2025 23:00:00 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.14339</link>
      <guid>https://doi.org/10.46298/fi.14339</guid>
      <author>Berthet, Pierre-Augustin</author>
      <dc:creator>Berthet, Pierre-Augustin</dc:creator>
      <content:encoded><![CDATA[Due to developments in quantum computing, classical asymmetric cryptography is at risk of being breached. Consequently, new Post-Quantum Cryptography (PQC) primitives using lattices are studied. Another point of scrutiny is the resilience of these new primitives to Side Channel Analysis (SCA), where an attacker can study physical leakages. In this work we discuss a SCA vulnerability due to the ciphertext malleability of some PQC primitives exposed by a work from Ravi et al. We propose a novel countermeasure to this vulnerability exploiting the same ciphertext malleability and discuss its practical application to several PQC primitives. We also extend the seminal work of Ravi et al. by detailing their attack on the different security levels of a post-quantum Key Encapsulation Mechanism (KEM), namely FrodoKEM. We also provide a generalisation of their attack to different parameters which could be used in future similar primitives.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>The fork and its role in unification of closure algebras</title>
      <description><![CDATA[We consider the two-pronged fork frame $F$ and the variety $\mathbf{Eq}(B_F)$ generated by its dual closure algebra $B_F$. We describe the finite projective algebras in $\mathbf{Eq}(B_F)$ and give a purely semantic proof that unification in $\mathbf{Eq}(B_F)$ is finitary and not unitary.]]></description>
      <pubDate>Tue, 30 Dec 2025 16:26:59 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12354</link>
      <guid>https://doi.org/10.46298/fi.12354</guid>
      <author>Düntsch, Ivo</author>
      <author>Dzik, Wojciech</author>
      <dc:creator>Düntsch, Ivo</dc:creator>
      <dc:creator>Dzik, Wojciech</dc:creator>
      <content:encoded><![CDATA[We consider the two-pronged fork frame $F$ and the variety $\mathbf{Eq}(B_F)$ generated by its dual closure algebra $B_F$. We describe the finite projective algebras in $\mathbf{Eq}(B_F)$ and give a purely semantic proof that unification in $\mathbf{Eq}(B_F)$ is finitary and not unitary.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Locally Integral Involutive PO-Semigroups</title>
      <description><![CDATA[We show that every locally integral involutive partially ordered semigroup (ipo-semigroup) $\mathbf A = (A,\le, \cdot, \sim,-)$, and in particular every locally integral involutive semiring, decomposes in a unique way into a family $\{\mathbf A_p : p\in A^+\}$ of integral ipo-monoids, which we call its integral components. In the semiring case, the integral components are unital semirings. Moreover, we show that there is a family of monoid homomorphisms $Φ= \{φ_{pq}: \mathbf A_p\to \mathbf A_q : p\le q\}$, indexed over the positive cone $(A^+,\le)$, so that the structure of $\mathbf A$ can be recovered as a glueing $\int_Φ\mathbf A_p$ of its integral components along $Φ$. Reciprocally, we give necessary and sufficient conditions so that the Płonka sum of any family of integral ipo-monoids $\{\mathbf A_p : p\in D\}$, indexed over a join-semilattice $(D,\lor)$ along a family of monoid homomorphisms $Φ$ is an ipo-semigroup.]]></description>
      <pubDate>Tue, 30 Dec 2025 16:23:33 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12449</link>
      <guid>https://doi.org/10.46298/fi.12449</guid>
      <author>Gil-Férez, José</author>
      <author>Jipsen, Peter</author>
      <author>Sugimoto, Melissa</author>
      <dc:creator>Gil-Férez, José</dc:creator>
      <dc:creator>Jipsen, Peter</dc:creator>
      <dc:creator>Sugimoto, Melissa</dc:creator>
      <content:encoded><![CDATA[We show that every locally integral involutive partially ordered semigroup (ipo-semigroup) $\mathbf A = (A,\le, \cdot, \sim,-)$, and in particular every locally integral involutive semiring, decomposes in a unique way into a family $\{\mathbf A_p : p\in A^+\}$ of integral ipo-monoids, which we call its integral components. In the semiring case, the integral components are unital semirings. Moreover, we show that there is a family of monoid homomorphisms $Φ= \{φ_{pq}: \mathbf A_p\to \mathbf A_q : p\le q\}$, indexed over the positive cone $(A^+,\le)$, so that the structure of $\mathbf A$ can be recovered as a glueing $\int_Φ\mathbf A_p$ of its integral components along $Φ$. Reciprocally, we give necessary and sufficient conditions so that the Płonka sum of any family of integral ipo-monoids $\{\mathbf A_p : p\in D\}$, indexed over a join-semilattice $(D,\lor)$ along a family of monoid homomorphisms $Φ$ is an ipo-semigroup.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A Theory of Conversion Relations for Prefixed Units of Measure</title>
      <description><![CDATA[Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as a class of ternary relations with both group-like and category-like properties. A hierarchy of subclasses is explored, each satisfying stronger useful algebraic properties than the preceding, culminating in a direct efficient conversion-by-rewriting algorithm.]]></description>
      <pubDate>Mon, 29 Dec 2025 14:39:25 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12436</link>
      <guid>https://doi.org/10.46298/fi.12436</guid>
      <author>Widemann, Baltasar Trancón y</author>
      <author>Lepper, Markus</author>
      <dc:creator>Widemann, Baltasar Trancón y</dc:creator>
      <dc:creator>Lepper, Markus</dc:creator>
      <content:encoded><![CDATA[Units of measure with prefixes and conversion rules are given a formal semantic model in terms of categorial group theory. Basic structures and both natural and contingent semantic operations are defined. Conversion rules are represented as a class of ternary relations with both group-like and category-like properties. A hierarchy of subclasses is explored, each satisfying stronger useful algebraic properties than the preceding, culminating in a direct efficient conversion-by-rewriting algorithm.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>The Index and Core of a Relation. With Applications to the Axiomatics of Relation Algebra</title>
      <description><![CDATA[We introduce the general notions of an index and a core of a relation. We postulate a limited form of the axiom of choice -- specifically that all partial equivalence relations have an index -- and explore the consequences of adding the axiom to standard axiom systems for point-free reasoning. Examples of the theorems we prove are that a core/index of a difunction is a bijection, and that the so-called ``all or nothing'' axiom used to facilitate pointwise reasoning is derivable from our axiom of choice.]]></description>
      <pubDate>Sat, 27 Dec 2025 12:59:02 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12245</link>
      <guid>https://doi.org/10.46298/fi.12245</guid>
      <author>Backhouse, Roland</author>
      <author>Voermans, Ed</author>
      <dc:creator>Backhouse, Roland</dc:creator>
      <dc:creator>Voermans, Ed</dc:creator>
      <content:encoded><![CDATA[We introduce the general notions of an index and a core of a relation. We postulate a limited form of the axiom of choice -- specifically that all partial equivalence relations have an index -- and explore the consequences of adding the axiom to standard axiom systems for point-free reasoning. Examples of the theorems we prove are that a core/index of a difunction is a bijection, and that the so-called ``all or nothing'' axiom used to facilitate pointwise reasoning is derivable from our axiom of choice.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Note on a Translation from First-Order Logic into the Calculus of Relations Preserving Validity and Finite Validity</title>
      <description><![CDATA[In this note, we give a linear-size translation from formulas of first-order logic into equations of the calculus of relations preserving validity and finite validity. Our translation also gives a linear-size conservative reduction from formulas of first-order logic into formulas of the three-variable fragment of first-order logic.]]></description>
      <pubDate>Sat, 27 Dec 2025 12:54:56 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12365</link>
      <guid>https://doi.org/10.46298/fi.12365</guid>
      <author>Nakamura, Yoshiki</author>
      <dc:creator>Nakamura, Yoshiki</dc:creator>
      <content:encoded><![CDATA[In this note, we give a linear-size translation from formulas of first-order logic into equations of the calculus of relations preserving validity and finite validity. Our translation also gives a linear-size conservative reduction from formulas of first-order logic into formulas of the three-variable fragment of first-order logic.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Translating Three-Variable First-Order Predicate Logic to Relation Algebra, Implemented using Z3</title>
      <description><![CDATA[This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its capabilities to enhance reliability, generate code, and expedite development. The resulting standalone Python program allows users to translate first-order logic formulas into relation algebra, eliminating the need to work with relation algebra explicitly. This paper outlines the theoretical background of first-order logic, relation algebra, and the translation process. It also describes the implementation details, including validation of the software tool using Z3 for testing correctness. By demonstrating the feasibility of utilizing first-order logic as an alternative language for expressing relation algebra, this tool paves the way for integrating first-order logic into tools traditionally relying on relation algebra as input.]]></description>
      <pubDate>Sat, 27 Dec 2025 12:53:47 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.11710</link>
      <guid>https://doi.org/10.46298/fi.11710</guid>
      <author>Brogni, Anthony</author>
      <author>Joosten, Sebastiaan J. C.</author>
      <dc:creator>Brogni, Anthony</dc:creator>
      <dc:creator>Joosten, Sebastiaan J. C.</dc:creator>
      <content:encoded><![CDATA[This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its capabilities to enhance reliability, generate code, and expedite development. The resulting standalone Python program allows users to translate first-order logic formulas into relation algebra, eliminating the need to work with relation algebra explicitly. This paper outlines the theoretical background of first-order logic, relation algebra, and the translation process. It also describes the implementation details, including validation of the software tool using Z3 for testing correctness. By demonstrating the feasibility of utilizing first-order logic as an alternative language for expressing relation algebra, this tool paves the way for integrating first-order logic into tools traditionally relying on relation algebra as input.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Comer Schemes, Relation Algebras, and the Flexible Atom Conjecture</title>
      <description><![CDATA[In this paper, we consider relational structures arising from Comer's finite field construction, where the cosets need not be sum free. These Comer schemes generalize the notion of a Ramsey scheme and may be of independent interest. As an application, we give the first finite representation of $34_{65}$. This leaves $33_{65}$ as the only remaining relation algebra in the family $N_{65}$ with a flexible atom that is not known to be finitely representable. Motivated by this, we complement our upper bounds with some lower bounds. Using a SAT solver, we show that $33_{65}$ is not finitely representable on fewer than $24$ points, and that $33_{65}$ does not admit a cyclic group representation on fewer than $120$ points. We also employ a SAT solver to show that $34_{65}$ is not representable on fewer than $24$ points.]]></description>
      <pubDate>Sat, 27 Dec 2025 12:52:49 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12328</link>
      <guid>https://doi.org/10.46298/fi.12328</guid>
      <author>Alm, Jeremy F.</author>
      <author>Andrews, David A.</author>
      <author>Levet, Michael</author>
      <dc:creator>Alm, Jeremy F.</dc:creator>
      <dc:creator>Andrews, David A.</dc:creator>
      <dc:creator>Levet, Michael</dc:creator>
      <content:encoded><![CDATA[In this paper, we consider relational structures arising from Comer's finite field construction, where the cosets need not be sum free. These Comer schemes generalize the notion of a Ramsey scheme and may be of independent interest. As an application, we give the first finite representation of $34_{65}$. This leaves $33_{65}$ as the only remaining relation algebra in the family $N_{65}$ with a flexible atom that is not known to be finitely representable. Motivated by this, we complement our upper bounds with some lower bounds. Using a SAT solver, we show that $33_{65}$ is not finitely representable on fewer than $24$ points, and that $33_{65}$ does not admit a cyclic group representation on fewer than $120$ points. We also employ a SAT solver to show that $34_{65}$ is not representable on fewer than $24$ points.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Dialectica Petri Nets</title>
      <description><![CDATA[The categorical modeling of Petri nets has received much attention recently. The Dialectica construction has also had its fair share of attention. We revisit the use of the Dialectica construction as a categorical model for Petri nets generalising the original application to suggest that Petri nets with different kinds of transitions can be modelled in the same categorical framework. Transitions representing truth-values, probabilities, rates or multiplicities, evaluated in different algebraic structures called lineales are useful and are modelled here in the same category. We investigate (categorical instances of) this generalised model and its connections to more recent models of categorical nets.]]></description>
      <pubDate>Tue, 23 Dec 2025 22:15:48 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.13125</link>
      <guid>https://doi.org/10.46298/fi.13125</guid>
      <author>Di Lavore, Elena</author>
      <author>Leal, Wilmer</author>
      <author>de Paiva, Valeria</author>
      <dc:creator>Di Lavore, Elena</dc:creator>
      <dc:creator>Leal, Wilmer</dc:creator>
      <dc:creator>de Paiva, Valeria</dc:creator>
      <content:encoded><![CDATA[The categorical modeling of Petri nets has received much attention recently. The Dialectica construction has also had its fair share of attention. We revisit the use of the Dialectica construction as a categorical model for Petri nets generalising the original application to suggest that Petri nets with different kinds of transitions can be modelled in the same categorical framework. Transitions representing truth-values, probabilities, rates or multiplicities, evaluated in different algebraic structures called lineales are useful and are modelled here in the same category. We investigate (categorical instances of) this generalised model and its connections to more recent models of categorical nets.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Runtime Repeated Recursion Unfolding in CHR: A Just-In-Time Online Program Optimization Strategy That Can Achieve Super-Linear Speedup</title>
      <description><![CDATA[We introduce a just-in-time runtime program transformation strategy based on repeated recursion unfolding. Our online program optimization generates several versions of a recursion differentiated by the minimal number of recursive steps covered. The base case of the recursion is ignored in our technique. Our method is introduced here on the basis of single linear direct recursive rules. When a recursive call is encountered at runtime, first an unfolder creates specializations of the associated recursive rule on-the-fly and then an interpreter applies these rules to the call. Our approach reduces the number of recursive rule applications to its logarithm at the expense of introducing a logarithmic number of generic unfolded rules. We prove correctness of our online optimization technique and determine its time complexity. For recursions which have enough simplifyable unfoldings, a super-linear is possible, i.e. speedup by more than a constant factor. The necessary simplification is problem-specific and has to be provided at compile-time. In our speedup analysis, we prove a sufficient condition as well as a sufficient and necessary condition for super-linear speedup relating the complexity of the recursive steps of the original rule and the unfolded rules. We have implemented an unfolder and meta-interpreter for runtime repeated recursion unfolding with just five rules in Constraint Handling Rules (CHR) embedded in Prolog. We illustrate the feasibility of our approach with simplifications, time complexity results and benchmarks for some basic tractable algorithms. The simplifications require some insight and were derived manually. The runtime improvement quickly reaches several orders of magnitude, consistent with the super-linear speedup predicted by our theorems.]]></description>
      <pubDate>Fri, 31 Oct 2025 17:04:34 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.11547</link>
      <guid>https://doi.org/10.46298/fi.11547</guid>
      <author>Fruehwirth, Thom</author>
      <dc:creator>Fruehwirth, Thom</dc:creator>
      <content:encoded><![CDATA[We introduce a just-in-time runtime program transformation strategy based on repeated recursion unfolding. Our online program optimization generates several versions of a recursion differentiated by the minimal number of recursive steps covered. The base case of the recursion is ignored in our technique. Our method is introduced here on the basis of single linear direct recursive rules. When a recursive call is encountered at runtime, first an unfolder creates specializations of the associated recursive rule on-the-fly and then an interpreter applies these rules to the call. Our approach reduces the number of recursive rule applications to its logarithm at the expense of introducing a logarithmic number of generic unfolded rules. We prove correctness of our online optimization technique and determine its time complexity. For recursions which have enough simplifyable unfoldings, a super-linear is possible, i.e. speedup by more than a constant factor. The necessary simplification is problem-specific and has to be provided at compile-time. In our speedup analysis, we prove a sufficient condition as well as a sufficient and necessary condition for super-linear speedup relating the complexity of the recursive steps of the original rule and the unfolded rules. We have implemented an unfolder and meta-interpreter for runtime repeated recursion unfolding with just five rules in Constraint Handling Rules (CHR) embedded in Prolog. We illustrate the feasibility of our approach with simplifications, time complexity results and benchmarks for some basic tractable algorithms. The simplifications require some insight and were derived manually. The runtime improvement quickly reaches several orders of magnitude, consistent with the super-linear speedup predicted by our theorems.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>The geodesic cover problem for butterfly networks</title>
      <description><![CDATA[A geodesic cover, also known as an isometric path cover, of a graph is a set of geodesics which cover the vertex set of the graph. An edge geodesic cover of a graph is a set of geodesics which cover the edge set of the graph. The geodesic (edge) cover number of a graph is the cardinality of a minimum (edge) geodesic cover. The (edge) geodesic cover problem of a graph is to find the (edge) geodesic cover number of the graph. Surprisingly, only partial solutions for these problems are available for most situations. In this paper we demonstrate that the geodesic cover number of the $r$-dimensional butterfly is $\lceil (2/3)2^r\rceil$ and that its edge geodesic cover number is $2^r$.]]></description>
      <pubDate>Mon, 27 Oct 2025 19:54:46 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.10201</link>
      <guid>https://doi.org/10.46298/fi.10201</guid>
      <author>Manuel, Paul</author>
      <author>Klavzar, Sandi</author>
      <author>Prabha, R.</author>
      <author>Arokiaraj, Andrew</author>
      <dc:creator>Manuel, Paul</dc:creator>
      <dc:creator>Klavzar, Sandi</dc:creator>
      <dc:creator>Prabha, R.</dc:creator>
      <dc:creator>Arokiaraj, Andrew</dc:creator>
      <content:encoded><![CDATA[A geodesic cover, also known as an isometric path cover, of a graph is a set of geodesics which cover the vertex set of the graph. An edge geodesic cover of a graph is a set of geodesics which cover the edge set of the graph. The geodesic (edge) cover number of a graph is the cardinality of a minimum (edge) geodesic cover. The (edge) geodesic cover problem of a graph is to find the (edge) geodesic cover number of the graph. Surprisingly, only partial solutions for these problems are available for most situations. In this paper we demonstrate that the geodesic cover number of the $r$-dimensional butterfly is $\lceil (2/3)2^r\rceil$ and that its edge geodesic cover number is $2^r$.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A concentration phenomenon for $h$-extra edge-connectivity reliability analysis of enhanced hypercubes $Q_{n,2}$ with exponentially many faulty links</title>
      <description><![CDATA[Reliability assessment of interconnection networks is critical to the design and maintenance of multiprocessor systems. The $(n, k)$-enhanced hypercube $Q_{n,k}$, as a variation of the hypercube $Q_{n}$, was proposed by Tzeng and Wei in 1991. As an extension of traditional edge-connectivity, $h$-extra edge-connectivity of a connected graph $G,$ $λ_h(G),$ is an essential parameter for evaluating the reliability of interconnection networks. This article intends to study the $h$-extra edge-connectivity of the $(n,2)$-enhanced hypercube $Q_{n,2}$. Suppose that the link malfunction of an interconnection network $Q_{n,2}$ does not isolate any subnetwork with no more than $h-1$ processors, the minimum number of these possible faulty links concentrates on a constant $2^{n-1}$ for each integer $\lceil\frac{11\times2^{n-1}}{48}\rceil \leq h \leq 2^{n-1}$ and $n\geq 9$. That is, for about $77.083\%$ of values where $h\leq2^{n-1},$ the corresponding $h$-extra edge-connectivity of $Q_{n,2}$, $λ_h(Q_{n,2})$, presents a concentration phenomenon. Moreover, the lower and upper bounds of $h$ mentioned above are both tight.]]></description>
      <pubDate>Sun, 26 Oct 2025 18:56:27 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.13487</link>
      <guid>https://doi.org/10.46298/fi.13487</guid>
      <author>Sun, Yali</author>
      <author>Zhang, Mingzu</author>
      <author>Feng, Xing</author>
      <author>Yang, Xing</author>
      <dc:creator>Sun, Yali</dc:creator>
      <dc:creator>Zhang, Mingzu</dc:creator>
      <dc:creator>Feng, Xing</dc:creator>
      <dc:creator>Yang, Xing</dc:creator>
      <content:encoded><![CDATA[Reliability assessment of interconnection networks is critical to the design and maintenance of multiprocessor systems. The $(n, k)$-enhanced hypercube $Q_{n,k}$, as a variation of the hypercube $Q_{n}$, was proposed by Tzeng and Wei in 1991. As an extension of traditional edge-connectivity, $h$-extra edge-connectivity of a connected graph $G,$ $λ_h(G),$ is an essential parameter for evaluating the reliability of interconnection networks. This article intends to study the $h$-extra edge-connectivity of the $(n,2)$-enhanced hypercube $Q_{n,2}$. Suppose that the link malfunction of an interconnection network $Q_{n,2}$ does not isolate any subnetwork with no more than $h-1$ processors, the minimum number of these possible faulty links concentrates on a constant $2^{n-1}$ for each integer $\lceil\frac{11\times2^{n-1}}{48}\rceil \leq h \leq 2^{n-1}$ and $n\geq 9$. That is, for about $77.083\%$ of values where $h\leq2^{n-1},$ the corresponding $h$-extra edge-connectivity of $Q_{n,2}$, $λ_h(Q_{n,2})$, presents a concentration phenomenon. Moreover, the lower and upper bounds of $h$ mentioned above are both tight.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Intersection Types for a Computational Lambda-Calculus with Global State</title>
      <description><![CDATA[We study the semantics of an untyped lambda-calculus equipped with operators representing read and write operations from and to a global store. We adopt the monadic approach to model side-effects and treat read and write as algebraic operations over a monad. We introduce operational and denotational semantics and a type assignment system of intersection types and prove that types are invariant under the reduction and expansion of term and state configurations. Finally, we characterize convergent terms via their typings.]]></description>
      <pubDate>Fri, 29 Aug 2025 11:25:31 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.10010</link>
      <guid>https://doi.org/10.46298/fi.10010</guid>
      <author>de'Liguoro, Ugo</author>
      <author>Treglia, Riccardo</author>
      <dc:creator>de'Liguoro, Ugo</dc:creator>
      <dc:creator>Treglia, Riccardo</dc:creator>
      <content:encoded><![CDATA[We study the semantics of an untyped lambda-calculus equipped with operators representing read and write operations from and to a global store. We adopt the monadic approach to model side-effects and treat read and write as algebraic operations over a monad. We introduce operational and denotational semantics and a type assignment system of intersection types and prove that types are invariant under the reduction and expansion of term and state configurations. Finally, we characterize convergent terms via their typings.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Demystifying $μ$</title>
      <description><![CDATA[We explore the theory of illfounded and cyclic proofs for the propositional modal $μ$-calculus. A fine analysis of provability for classical and intuitionistic modal logic provides a novel bridge between finitary, cyclic and illfounded conceptions of proof and re-enforces the importance of two normal form theorems for the logic: guardedness and disjunctiveness.]]></description>
      <pubDate>Thu, 28 Aug 2025 15:02:16 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12773</link>
      <guid>https://doi.org/10.46298/fi.12773</guid>
      <author>Afshari, Bahareh</author>
      <author>Leigh, Graham E.</author>
      <author>Turata, Guillermo Menèndez</author>
      <dc:creator>Afshari, Bahareh</dc:creator>
      <dc:creator>Leigh, Graham E.</dc:creator>
      <dc:creator>Turata, Guillermo Menèndez</dc:creator>
      <content:encoded><![CDATA[We explore the theory of illfounded and cyclic proofs for the propositional modal $μ$-calculus. A fine analysis of provability for classical and intuitionistic modal logic provides a novel bridge between finitary, cyclic and illfounded conceptions of proof and re-enforces the importance of two normal form theorems for the logic: guardedness and disjunctiveness.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Peano Arithmetic and $μ$MALL</title>
      <description><![CDATA[Formal theories of arithmetic have traditionally been based on either classical or intuitionistic logic, leading to the development of Peano and Heyting arithmetic, respectively. We propose to use $μ$MALL as a formal theory of arithmetic based on linear logic. This formal system is presented as a sequent calculus proof system that extends the standard proof system for multiplicative-additive linear logic (MALL) with the addition of the logical connectives universal and existential quantifiers (first-order quantifiers), term equality and non-equality, and the least and greatest fixed point operators. We first demonstrate how functions defined using $μ$MALL relational specifications can be computed using a simple proof search algorithm. By incorporating weakening and contraction into $μ$MALL, we obtain $μ$LK+, a natural candidate for a classical sequent calculus for arithmetic. While important proof theory results are still lacking for $μ$LK+ (including cut-elimination and the completeness of focusing), we prove that $μ$LK+ is consistent and that it contains Peano arithmetic. We also prove some conservativity results regarding $μ$LK+ over $μ$MALL.]]></description>
      <pubDate>Thu, 28 Aug 2025 15:01:43 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12736</link>
      <guid>https://doi.org/10.46298/fi.12736</guid>
      <author>Manighetti, Matteo</author>
      <author>Miller, Dale</author>
      <dc:creator>Manighetti, Matteo</dc:creator>
      <dc:creator>Miller, Dale</dc:creator>
      <content:encoded><![CDATA[Formal theories of arithmetic have traditionally been based on either classical or intuitionistic logic, leading to the development of Peano and Heyting arithmetic, respectively. We propose to use $μ$MALL as a formal theory of arithmetic based on linear logic. This formal system is presented as a sequent calculus proof system that extends the standard proof system for multiplicative-additive linear logic (MALL) with the addition of the logical connectives universal and existential quantifiers (first-order quantifiers), term equality and non-equality, and the least and greatest fixed point operators. We first demonstrate how functions defined using $μ$MALL relational specifications can be computed using a simple proof search algorithm. By incorporating weakening and contraction into $μ$MALL, we obtain $μ$LK+, a natural candidate for a classical sequent calculus for arithmetic. While important proof theory results are still lacking for $μ$LK+ (including cut-elimination and the completeness of focusing), we prove that $μ$LK+ is consistent and that it contains Peano arithmetic. We also prove some conservativity results regarding $μ$LK+ over $μ$MALL.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Relative fixed points of functors</title>
      <description><![CDATA[We show how the relatively initial or relatively terminal fixed points for a well-behaved functor $F$ form a pair of adjoint functors between $F$-coalgebras and $F$-algebras. We use the language of locally presentable categories to find sufficient conditions for existence of this adjunction. We show that relative fixed points may be characterized as (co)equalizers of the free (co)monad on $F$. In particular, when $F$ is a polynomial functor on $\mathsf{Set}$ the relative fixed points are a quotient or subset of the free term algebra or the cofree term coalgebra. We give examples of the relative fixed points for polynomial functors and an example which is the Sierpinski carpet. Lastly, we prove a general preservation result for relative fixed points.]]></description>
      <pubDate>Thu, 28 Aug 2025 15:01:12 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12374</link>
      <guid>https://doi.org/10.46298/fi.12374</guid>
      <author>Schoen, Ezra</author>
      <author>Master, Jade</author>
      <author>Kupke, Clemens</author>
      <dc:creator>Schoen, Ezra</dc:creator>
      <dc:creator>Master, Jade</dc:creator>
      <dc:creator>Kupke, Clemens</dc:creator>
      <content:encoded><![CDATA[We show how the relatively initial or relatively terminal fixed points for a well-behaved functor $F$ form a pair of adjoint functors between $F$-coalgebras and $F$-algebras. We use the language of locally presentable categories to find sufficient conditions for existence of this adjunction. We show that relative fixed points may be characterized as (co)equalizers of the free (co)monad on $F$. In particular, when $F$ is a polynomial functor on $\mathsf{Set}$ the relative fixed points are a quotient or subset of the free term algebra or the cofree term coalgebra. We give examples of the relative fixed points for polynomial functors and an example which is the Sierpinski carpet. Lastly, we prove a general preservation result for relative fixed points.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Tractable and Intractable Entailment Problems in Separation Logic with Inductively Defined Predicates</title>
      <description><![CDATA[We establish various complexity results for the entailment problem between formulas in Separation Logic with user-defined predicates denoting recursive data structures. The considered fragments are characterized by syntactic conditions on the inductive rules that define the semantics of the predicates. We focus on so-called P-rules, which are similar to (but simpler than) the PCE rules introduced by Iosif et al. in 2013. In particular, for a specific fragment where predicates are defined by so-called loc-deterministic inductive rules, we devise a sound and complete cyclic proof procedure running in polynomial time. Several complexity lower bounds are provided, showing that any relaxing of the provided conditions makes the problem intractable.]]></description>
      <pubDate>Wed, 16 Jul 2025 11:30:21 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.11318</link>
      <guid>https://doi.org/10.46298/fi.11318</guid>
      <author>Echenim, Mnacho</author>
      <author>Peltier, Nicolas</author>
      <dc:creator>Echenim, Mnacho</dc:creator>
      <dc:creator>Peltier, Nicolas</dc:creator>
      <content:encoded><![CDATA[We establish various complexity results for the entailment problem between formulas in Separation Logic with user-defined predicates denoting recursive data structures. The considered fragments are characterized by syntactic conditions on the inductive rules that define the semantics of the predicates. We focus on so-called P-rules, which are similar to (but simpler than) the PCE rules introduced by Iosif et al. in 2013. In particular, for a specific fragment where predicates are defined by so-called loc-deterministic inductive rules, we devise a sound and complete cyclic proof procedure running in polynomial time. Several complexity lower bounds are provided, showing that any relaxing of the provided conditions makes the problem intractable.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On the Computational Power of Particle Methods</title>
      <description><![CDATA[We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of problems it can solve. Automata theory allows describing the computational power of abstract machines (automata) and the problems they can solve. At the top of the Chomsky hierarchy of formal languages and grammars are Turing machines, which resemble the concept on which most modern computers are built. Although particle methods can be interpreted as automata based on their formal definition, their computational power has so far not been studied. We address this by analyzing Turing completeness of particle methods. In particular, we prove two sets of restrictions under which a particle method is still Turing powerful, and we show when it loses Turing powerfulness. This contributes to understanding the theoretical foundations of particle methods and provides insight into the powerfulness of computer simulations.]]></description>
      <pubDate>Wed, 16 Jul 2025 11:26:07 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.11227</link>
      <guid>https://doi.org/10.46298/fi.11227</guid>
      <author>Pahlke, Johannes</author>
      <author>Sbalzarini, Ivo F.</author>
      <dc:creator>Pahlke, Johannes</dc:creator>
      <dc:creator>Sbalzarini, Ivo F.</dc:creator>
      <content:encoded><![CDATA[We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of problems it can solve. Automata theory allows describing the computational power of abstract machines (automata) and the problems they can solve. At the top of the Chomsky hierarchy of formal languages and grammars are Turing machines, which resemble the concept on which most modern computers are built. Although particle methods can be interpreted as automata based on their formal definition, their computational power has so far not been studied. We address this by analyzing Turing completeness of particle methods. In particular, we prove two sets of restrictions under which a particle method is still Turing powerful, and we show when it loses Turing powerfulness. This contributes to understanding the theoretical foundations of particle methods and provides insight into the powerfulness of computer simulations.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Constructing disjoint Steiner trees in Sierpiński graphs</title>
      <description><![CDATA[Let $G$ be a graph and $S\subseteq V(G)$ with $|S|\geq 2$. Then the trees $T_1, T_2, \cdots, T_\ell$ in $G$ are \emph{internally disjoint Steiner trees} connecting $S$ (or $S$-Steiner trees) if $E(T_i) \cap E(T_j )=\emptyset$ and $V(T_i)\cap V(T_j)=S$ for every pair of distinct integers $i,j$, $1 \leq i, j \leq \ell$. Similarly, if we only have the condition $E(T_i) \cap E(T_j )=\emptyset$ but without the condition $V(T_i)\cap V(T_j)=S$, then they are \emph{edge-disjoint Steiner trees}. The \emph{generalized $k$-connectivity}, denoted by $κ_k(G)$, of a graph $G$, is defined as $κ_k(G)=\min\{κ_G(S)|S \subseteq V(G) \ \textrm{and} \ |S|=k \}$, where $κ_G(S)$ is the maximum number of internally disjoint $S$-Steiner trees. The \emph{generalized local edge-connectivity} $λ_{G}(S)$ is the maximum number of edge-disjoint Steiner trees connecting $S$ in $G$. The {\it generalized $k$-edge-connectivity} $λ_k(G)$ of $G$ is defined as $λ_k(G)=\min\{λ_{G}(S)\,|\,S\subseteq V(G) \ and \ |S|=k\}$. These measures are generalizations of the concepts of connectivity and edge-connectivity, and they and can be used as measures of vulnerability of networks. It is, in general, difficult to compute these generalized connectivities. However, there are precise results for some special classes of graphs. In this paper, we obtain the exact value of $λ_{k}(S(n,\ell))$ for $3\leq k\leq \ell^n$, and the exact value of $κ_{k}(S(n,\ell))$ for $3\leq k\leq \ell$, where $S(n, \ell)$ is the Sierpiński graphs with order $\ell^n$. As a direct consequence, these graphs provide additional interesting examples when $λ_{k}(S(n,\ell))=κ_{k}(S(n,\ell))$. We also study the some network properties of Sierpiński graphs.]]></description>
      <pubDate>Sat, 05 Jul 2025 18:25:54 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.12478</link>
      <guid>https://doi.org/10.46298/fi.12478</guid>
      <author>Yang, Chenxu</author>
      <author>Li, Ping</author>
      <author>Mao, Yaping</author>
      <author>Cheng, Eddie</author>
      <author>Klasing, Ralf</author>
      <dc:creator>Yang, Chenxu</dc:creator>
      <dc:creator>Li, Ping</dc:creator>
      <dc:creator>Mao, Yaping</dc:creator>
      <dc:creator>Cheng, Eddie</dc:creator>
      <dc:creator>Klasing, Ralf</dc:creator>
      <content:encoded><![CDATA[Let $G$ be a graph and $S\subseteq V(G)$ with $|S|\geq 2$. Then the trees $T_1, T_2, \cdots, T_\ell$ in $G$ are \emph{internally disjoint Steiner trees} connecting $S$ (or $S$-Steiner trees) if $E(T_i) \cap E(T_j )=\emptyset$ and $V(T_i)\cap V(T_j)=S$ for every pair of distinct integers $i,j$, $1 \leq i, j \leq \ell$. Similarly, if we only have the condition $E(T_i) \cap E(T_j )=\emptyset$ but without the condition $V(T_i)\cap V(T_j)=S$, then they are \emph{edge-disjoint Steiner trees}. The \emph{generalized $k$-connectivity}, denoted by $κ_k(G)$, of a graph $G$, is defined as $κ_k(G)=\min\{κ_G(S)|S \subseteq V(G) \ \textrm{and} \ |S|=k \}$, where $κ_G(S)$ is the maximum number of internally disjoint $S$-Steiner trees. The \emph{generalized local edge-connectivity} $λ_{G}(S)$ is the maximum number of edge-disjoint Steiner trees connecting $S$ in $G$. The {\it generalized $k$-edge-connectivity} $λ_k(G)$ of $G$ is defined as $λ_k(G)=\min\{λ_{G}(S)\,|\,S\subseteq V(G) \ and \ |S|=k\}$. These measures are generalizations of the concepts of connectivity and edge-connectivity, and they and can be used as measures of vulnerability of networks. It is, in general, difficult to compute these generalized connectivities. However, there are precise results for some special classes of graphs. In this paper, we obtain the exact value of $λ_{k}(S(n,\ell))$ for $3\leq k\leq \ell^n$, and the exact value of $κ_{k}(S(n,\ell))$ for $3\leq k\leq \ell$, where $S(n, \ell)$ is the Sierpiński graphs with order $\ell^n$. As a direct consequence, these graphs provide additional interesting examples when $λ_{k}(S(n,\ell))=κ_{k}(S(n,\ell))$. We also study the some network properties of Sierpiński graphs.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Equational theory of ordinals with addition and left multiplication by $ω$</title>
      <description><![CDATA[We show that the equational theory of the structure $\langle ω^ω: (x,y)\mapsto x+y, x\mapsto ωx \rangle $ is finitely axiomatizable and give a simple axiom schema when the domain is the set of transfinite ordinals. We give an algorithm that given a pair of terms $(E,F)$ decides in linear time with respect of their common length whether or not $E=F$ is a consequence of the axioms.]]></description>
      <pubDate>Sat, 05 Jul 2025 18:22:43 +0000</pubDate>
      <link>https://doi.org/10.46298/fi.13734</link>
      <guid>https://doi.org/10.46298/fi.13734</guid>
      <author>Choffrut, Christian</author>
      <dc:creator>Choffrut, Christian</dc:creator>
      <content:encoded><![CDATA[We show that the equational theory of the structure $\langle ω^ω: (x,y)\mapsto x+y, x\mapsto ωx \rangle $ is finitely axiomatizable and give a simple axiom schema when the domain is the set of transfinite ordinals. We give an algorithm that given a pair of terms $(E,F)$ decides in linear time with respect of their common length whether or not $E=F$ is a consequence of the axioms.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Maximum Centre-Disjoint Mergeable Disks</title>
      <description><![CDATA[Given a set of disks in the plane, the goal of the problem studied in this paper is to choose a subset of these disks such that none of its members contains the centre of any other. Each disk not in this subset must be merged with one of its nearby disks that is, increasing the latter's radius. This problem has applications in labelling rotating maps and in visualizing the distribution of entities in static maps. We prove that this problem is NP-hard. We also present an ILP formulation for this problem, and a polynomial-time algorithm for the special case in which the centres of all disks are on a line.]]></description>
      <pubDate>Wed, 14 May 2025 09:23:23 +0000</pubDate>
      <link>https://fi.episciences.org/14990</link>
      <guid>https://fi.episciences.org/14990</guid>
      <author>Rudi, Ali Gholami</author>
      <dc:creator>Rudi, Ali Gholami</dc:creator>
      <content:encoded><![CDATA[Given a set of disks in the plane, the goal of the problem studied in this paper is to choose a subset of these disks such that none of its members contains the centre of any other. Each disk not in this subset must be merged with one of its nearby disks that is, increasing the latter's radius. This problem has applications in labelling rotating maps and in visualizing the distribution of entities in static maps. We prove that this problem is NP-hard. We also present an ILP formulation for this problem, and a polynomial-time algorithm for the special case in which the centres of all disks are on a line.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Single-sample versus case-control sampling scheme for Positive Unlabeled data: the story of two scenarios</title>
      <description><![CDATA[In the paper we argue that performance of the classifiers based on Empirical Risk Minimization (ERM) for positive unlabeled data, which are designed for case-control sampling scheme may significantly deteriorate when applied to a single-sample scenario. We reveal why their behavior depends, in all but very specific cases, on the scenario. Also, we introduce a single-sample case analogue of the popular non-negative risk classifier designed for case-control data and compare its performance with the original proposal. We show that the significant differences occur between them, especiall when half or more positive of observations are labeled. The opposite case when ERM minimizer designed for the case-control case is applied for single-sample data is also considered and similar conclusions are drawn. Taking into account difference of scenarios requires a sole, but crucial, change in the definition of the Empirical Risk.]]></description>
      <pubDate>Wed, 14 May 2025 09:22:54 +0000</pubDate>
      <link>https://fi.episciences.org/14991</link>
      <guid>https://fi.episciences.org/14991</guid>
      <author>Mielniczuk, Jan</author>
      <author>Wawrzeńczyk, Adam</author>
      <dc:creator>Mielniczuk, Jan</dc:creator>
      <dc:creator>Wawrzeńczyk, Adam</dc:creator>
      <content:encoded><![CDATA[In the paper we argue that performance of the classifiers based on Empirical Risk Minimization (ERM) for positive unlabeled data, which are designed for case-control sampling scheme may significantly deteriorate when applied to a single-sample scenario. We reveal why their behavior depends, in all but very specific cases, on the scenario. Also, we introduce a single-sample case analogue of the popular non-negative risk classifier designed for case-control data and compare its performance with the original proposal. We show that the significant differences occur between them, especiall when half or more positive of observations are labeled. The opposite case when ERM minimizer designed for the case-control case is applied for single-sample data is also considered and similar conclusions are drawn. Taking into account difference of scenarios requires a sole, but crucial, change in the definition of the Empirical Risk.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On Completely Edge-Independent Spanning Trees in Locally Twisted Cubes</title>
      <description><![CDATA[A network can contain numerous spanning trees. If two spanning trees $T_i,T_j$ do not share any common edges, $T_i$ and $T_j$ are said to be pairwisely edge-disjoint. For spanning trees $T_1, T_2, ..., T_m$, if every two of them are pairwisely edge-disjoint, they are called completely edge-independent spanning trees (CEISTs for short). CEISTs can facilitate many network functionalities, and constructing CEISTs as maximally allowed as possible in a given network is a worthy undertaking. In this paper, we establish the maximal number of CEISTs in the locally twisted cube network, and propose an algorithm to construct $\lfloor \frac{n}{2} \rfloor$ CEISTs in $LTQ_n$, the $n$-dimensional locally twisted cube. The proposed algorithm has been actually implemented, and we present the outputs. Network broadcasting in the $LTQ_n$ was simulated using $\lfloor\frac{n}{2}\rfloor$ CEISTs, and the performance compared with broadcasting using a single tree.]]></description>
      <pubDate>Wed, 14 May 2025 09:22:24 +0000</pubDate>
      <link>https://fi.episciences.org/15670</link>
      <guid>https://fi.episciences.org/15670</guid>
      <author>Li, Xiaorui</author>
      <author>Cheng, Baolei</author>
      <author>Fan, Jianxi</author>
      <author>Wang, Yan</author>
      <author>Wang, Dajin</author>
      <dc:creator>Li, Xiaorui</dc:creator>
      <dc:creator>Cheng, Baolei</dc:creator>
      <dc:creator>Fan, Jianxi</dc:creator>
      <dc:creator>Wang, Yan</dc:creator>
      <dc:creator>Wang, Dajin</dc:creator>
      <content:encoded><![CDATA[A network can contain numerous spanning trees. If two spanning trees $T_i,T_j$ do not share any common edges, $T_i$ and $T_j$ are said to be pairwisely edge-disjoint. For spanning trees $T_1, T_2, ..., T_m$, if every two of them are pairwisely edge-disjoint, they are called completely edge-independent spanning trees (CEISTs for short). CEISTs can facilitate many network functionalities, and constructing CEISTs as maximally allowed as possible in a given network is a worthy undertaking. In this paper, we establish the maximal number of CEISTs in the locally twisted cube network, and propose an algorithm to construct $\lfloor \frac{n}{2} \rfloor$ CEISTs in $LTQ_n$, the $n$-dimensional locally twisted cube. The proposed algorithm has been actually implemented, and we present the outputs. Network broadcasting in the $LTQ_n$ was simulated using $\lfloor\frac{n}{2}\rfloor$ CEISTs, and the performance compared with broadcasting using a single tree.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>All Graphs with at most 8 nodes are 2-interval-PCGs</title>
      <description><![CDATA[A graph G is a multi-interval PCG if there exist an edge weighted tree T with non-negative real values and disjoint intervals of the non-negative real half-line such that each node of G is uniquely associated to a leaf of T and there is an edge between two nodes in G if and only if the weighted distance between their corresponding leaves in T lies within any such intervals. If the number of intervals is k, then we call the graph a k-interval-PCG; in symbols, G = k-interval-PCG (T, I1, . . . , Ik). It is known that 2-interval-PCGs do not contain all graphs and the smallest known graph outside this class has 135 nodes. Here we prove that all graphs with at most 8 nodes are 2-interval-PCGs, so doing one step towards the determination of the smallest value of n such that there exists an n node graph that is not a 2-interval-PCG.]]></description>
      <pubDate>Wed, 14 May 2025 09:21:19 +0000</pubDate>
      <link>https://fi.episciences.org/15029</link>
      <guid>https://fi.episciences.org/15029</guid>
      <author>Calamoneri, Tiziana</author>
      <author>Monti, Angelo</author>
      <author>Petroni, Fabrizio</author>
      <dc:creator>Calamoneri, Tiziana</dc:creator>
      <dc:creator>Monti, Angelo</dc:creator>
      <dc:creator>Petroni, Fabrizio</dc:creator>
      <content:encoded><![CDATA[A graph G is a multi-interval PCG if there exist an edge weighted tree T with non-negative real values and disjoint intervals of the non-negative real half-line such that each node of G is uniquely associated to a leaf of T and there is an edge between two nodes in G if and only if the weighted distance between their corresponding leaves in T lies within any such intervals. If the number of intervals is k, then we call the graph a k-interval-PCG; in symbols, G = k-interval-PCG (T, I1, . . . , Ik). It is known that 2-interval-PCGs do not contain all graphs and the smallest known graph outside this class has 135 nodes. Here we prove that all graphs with at most 8 nodes are 2-interval-PCGs, so doing one step towards the determination of the smallest value of n such that there exists an n node graph that is not a 2-interval-PCG.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Proving Confluence in the Confluence Framework with CONFident</title>
      <description><![CDATA[This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically prove and disprove confluence of *Generalized Term Rewriting Systems*, where (i) only selected arguments of function symbols can be rewritten and (ii) a rather general class of conditional rules can be used. This includes, as particular cases, several variants of rewrite systems such as (context-sensitive) *term rewriting systems*, *string rewriting systems*, and (context-sensitive) *conditional term rewriting systems*. The divide-and-conquer modular strategy allows us to combine in a proof tree different techniques for proving confluence, including modular decompositions, checking joinability of (conditional) critical and variable pairs, transformations, etc., and auxiliary tasks required by them, e.g., joinability of terms, joinability of conditional pairs, etc.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:46:14 +0000</pubDate>
      <link>https://fi.episciences.org/14128</link>
      <guid>https://fi.episciences.org/14128</guid>
      <author>Gutiérrez, Raúl</author>
      <author>Lucas, Salvador</author>
      <author>Vítores, Miguel</author>
      <dc:creator>Gutiérrez, Raúl</dc:creator>
      <dc:creator>Lucas, Salvador</dc:creator>
      <dc:creator>Vítores, Miguel</dc:creator>
      <content:encoded><![CDATA[This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically prove and disprove confluence of *Generalized Term Rewriting Systems*, where (i) only selected arguments of function symbols can be rewritten and (ii) a rather general class of conditional rules can be used. This includes, as particular cases, several variants of rewrite systems such as (context-sensitive) *term rewriting systems*, *string rewriting systems*, and (context-sensitive) *conditional term rewriting systems*. The divide-and-conquer modular strategy allows us to combine in a proof tree different techniques for proving confluence, including modular decompositions, checking joinability of (conditional) critical and variable pairs, transformations, etc., and auxiliary tasks required by them, e.g., joinability of terms, joinability of conditional pairs, etc.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On Complexity Bounds and Confluence of Parallel Term Rewriting</title>
      <description><![CDATA[We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. Our approach to find lower bounds requires confluence of the parallel-innermost rewrite relation, thus we also provide effective sufficient criteria for proving confluence. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool AProVE and by experiments on numerous benchmarks from the literature.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:45:51 +0000</pubDate>
      <link>https://fi.episciences.org/14207</link>
      <guid>https://fi.episciences.org/14207</guid>
      <author>Baudon, Thaïs</author>
      <author>Fuhs, Carsten</author>
      <author>Gonnord, Laure</author>
      <dc:creator>Baudon, Thaïs</dc:creator>
      <dc:creator>Fuhs, Carsten</dc:creator>
      <dc:creator>Gonnord, Laure</dc:creator>
      <content:encoded><![CDATA[We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques to derive both upper and lower bounds on parallel complexity of rewriting that enable a direct reuse of existing techniques for sequential complexity. Our approach to find lower bounds requires confluence of the parallel-innermost rewrite relation, thus we also provide effective sufficient criteria for proving confluence. The applicability and the precision of the method are demonstrated by the relatively light effort in extending the program analysis tool AProVE and by experiments on numerous benchmarks from the literature.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Relation-Algebraic Verification of Disjoint-Set Forests</title>
      <description><![CDATA[This paper studies how to use relation algebras, which are useful for high-level specification and verification, for proving the correctness of lower-level array-based implementations of algorithms. We give a simple relation-algebraic semantics of read and write operations on associative arrays. The array operations seamlessly integrate with assignments in computation models supporting while-programs. As a result, relation algebras can be used for verifying programs with associative arrays. We verify the correctness of an array-based implementation of disjoint-set forests using the union-by-rank strategy and find operations with path compression, path splitting and path halving. All results are formally proved in Isabelle/HOL. This paper is an extended version of [1].]]></description>
      <pubDate>Sun, 10 Nov 2024 10:42:39 +0000</pubDate>
      <link>https://fi.episciences.org/13951</link>
      <guid>https://fi.episciences.org/13951</guid>
      <author>Guttmann, Walter</author>
      <dc:creator>Guttmann, Walter</dc:creator>
      <content:encoded><![CDATA[This paper studies how to use relation algebras, which are useful for high-level specification and verification, for proving the correctness of lower-level array-based implementations of algorithms. We give a simple relation-algebraic semantics of read and write operations on associative arrays. The array operations seamlessly integrate with assignments in computation models supporting while-programs. As a result, relation algebras can be used for verifying programs with associative arrays. We verify the correctness of an array-based implementation of disjoint-set forests using the union-by-rank strategy and find operations with path compression, path splitting and path halving. All results are formally proved in Isabelle/HOL. This paper is an extended version of [1].]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Global types and event structure semantics for asynchronous multiparty sessions</title>
      <description><![CDATA[We propose an interpretation of multiparty sessions with asynchronous communication as Flow Event Structures. We introduce a new notion of global type for asynchronous multiparty sessions, ensuring the expected properties for sessions, including progress. Our global types, which reflect asynchrony more directly than standard global types and are more permissive, are themselves interpreted as Prime Event Structures. The main result is that the Event Structure interpretation of a session is equivalent, when the session is typable, to the Event Structure interpretation of its global type.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:42:14 +0000</pubDate>
      <link>https://fi.episciences.org/13946</link>
      <guid>https://fi.episciences.org/13946</guid>
      <author>Castellani, Ilaria</author>
      <author>Dezani-Ciancaglini, Mariangiola</author>
      <author>Giannini, Paola</author>
      <dc:creator>Castellani, Ilaria</dc:creator>
      <dc:creator>Dezani-Ciancaglini, Mariangiola</dc:creator>
      <dc:creator>Giannini, Paola</dc:creator>
      <content:encoded><![CDATA[We propose an interpretation of multiparty sessions with asynchronous communication as Flow Event Structures. We introduce a new notion of global type for asynchronous multiparty sessions, ensuring the expected properties for sessions, including progress. Our global types, which reflect asynchrony more directly than standard global types and are more permissive, are themselves interpreted as Prime Event Structures. The main result is that the Event Structure interpretation of a session is equivalent, when the session is typable, to the Event Structure interpretation of its global type.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Optimal local identifying and local locating-dominating codes</title>
      <description><![CDATA[We introduce two new classes of covering codes in graphs for every positive integer $r$. These new codes are called local $r$-identifying and local $r$-locating-dominating codes and they are derived from $r$-identifying and $r$-locating-dominating codes, respectively. We study the sizes of optimal local 1-identifying codes in binary hypercubes. We obtain lower and upper bounds that are asymptotically tight. Together the bounds show that the cost of changing covering codes into local 1-identifying codes is negligible. For some small $n$ optimal constructions are obtained. Moreover, the upper bound is obtained by a linear code construction. Also, we study the densities of optimal local 1-identifying codes and local 1-locating-dominating codes in the infinite square grid, the hexagonal grid, the triangular grid, and the king grid. We prove that seven out of eight of our constructions have optimal densities.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:30:05 +0000</pubDate>
      <link>https://fi.episciences.org/13881</link>
      <guid>https://fi.episciences.org/13881</guid>
      <author>Herva, Pyry</author>
      <author>Laihonen, Tero</author>
      <author>Lehtilä, Tuomo</author>
      <dc:creator>Herva, Pyry</dc:creator>
      <dc:creator>Laihonen, Tero</dc:creator>
      <dc:creator>Lehtilä, Tuomo</dc:creator>
      <content:encoded><![CDATA[We introduce two new classes of covering codes in graphs for every positive integer $r$. These new codes are called local $r$-identifying and local $r$-locating-dominating codes and they are derived from $r$-identifying and $r$-locating-dominating codes, respectively. We study the sizes of optimal local 1-identifying codes in binary hypercubes. We obtain lower and upper bounds that are asymptotically tight. Together the bounds show that the cost of changing covering codes into local 1-identifying codes is negligible. For some small $n$ optimal constructions are obtained. Moreover, the upper bound is obtained by a linear code construction. Also, we study the densities of optimal local 1-identifying codes and local 1-locating-dominating codes in the infinite square grid, the hexagonal grid, the triangular grid, and the king grid. We prove that seven out of eight of our constructions have optimal densities.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Finding codes on infinite grids automatically</title>
      <description><![CDATA[We apply automata theory and Karp's minimum mean weight cycle algorithm to minimum density problems in coding theory. Using this method, we find the new upper bound $53/126 \approx 0.4206$ for the minimum density of an identifying code on the infinite hexagonal grid, down from the previous record of $3/7 \approx 0.4286$.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:29:41 +0000</pubDate>
      <link>https://fi.episciences.org/13912</link>
      <guid>https://fi.episciences.org/13912</guid>
      <author>Salo, Ville</author>
      <author>Törmä, Ilkka</author>
      <dc:creator>Salo, Ville</dc:creator>
      <dc:creator>Törmä, Ilkka</dc:creator>
      <content:encoded><![CDATA[We apply automata theory and Karp's minimum mean weight cycle algorithm to minimum density problems in coding theory. Using this method, we find the new upper bound $53/126 \approx 0.4206$ for the minimum density of an identifying code on the infinite hexagonal grid, down from the previous record of $3/7 \approx 0.4286$.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Complexity and equivalency of multiset dimension and ID-colorings</title>
      <description><![CDATA[This investigation is firstly focused into showing that two metric parameters represent the same object in graph theory. That is, we prove that the multiset resolving sets and the ID-colorings of graphs are the same thing. We also consider some computational and combinatorial problems of the multiset dimension, or equivalently, the ID-number of graphs. We prove that the decision problem concerning finding the multiset dimension of graphs is NP-complete. We consider the multiset dimension of king grids and prove that it is bounded above by 4. We also give a characterization of the strong product graphs with one factor being a complete graph, and whose multiset dimension is not infinite.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:29:10 +0000</pubDate>
      <link>https://fi.episciences.org/13918</link>
      <guid>https://fi.episciences.org/13918</guid>
      <author>Hakanen, Anni</author>
      <author>Yero, Ismael G.</author>
      <dc:creator>Hakanen, Anni</dc:creator>
      <dc:creator>Yero, Ismael G.</dc:creator>
      <content:encoded><![CDATA[This investigation is firstly focused into showing that two metric parameters represent the same object in graph theory. That is, we prove that the multiset resolving sets and the ID-colorings of graphs are the same thing. We also consider some computational and combinatorial problems of the multiset dimension, or equivalently, the ID-number of graphs. We prove that the decision problem concerning finding the multiset dimension of graphs is NP-complete. We consider the multiset dimension of king grids and prove that it is bounded above by 4. We also give a characterization of the strong product graphs with one factor being a complete graph, and whose multiset dimension is not infinite.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Strong regulatory graphs</title>
      <description><![CDATA[Logical modeling is a powerful tool in biology, offering a system-level understanding of the complex interactions that govern biological processes. A gap that hinders the scalability of logical models is the need to specify the update function of every vertex in the network depending on the status of its predecessors. To address this, we introduce in this paper the concept of strong regulation, where a vertex is only updated to active/inactive if all its predecessors agree in their influences; otherwise, it is set to ambiguous. We explore the interplay between active, inactive, and ambiguous influences in a network. We discuss the existence of phenotype attractors in such networks, where the status of some of the variables is fixed to active/inactive, while the others can have an arbitrary status, including ambiguous.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:28:44 +0000</pubDate>
      <link>https://fi.episciences.org/12377</link>
      <guid>https://fi.episciences.org/12377</guid>
      <author>Gustafsson, Patric</author>
      <author>Petre, Ion</author>
      <dc:creator>Gustafsson, Patric</dc:creator>
      <dc:creator>Petre, Ion</dc:creator>
      <content:encoded><![CDATA[Logical modeling is a powerful tool in biology, offering a system-level understanding of the complex interactions that govern biological processes. A gap that hinders the scalability of logical models is the need to specify the update function of every vertex in the network depending on the status of its predecessors. To address this, we introduce in this paper the concept of strong regulation, where a vertex is only updated to active/inactive if all its predecessors agree in their influences; otherwise, it is set to ambiguous. We explore the interplay between active, inactive, and ambiguous influences in a network. We discuss the existence of phenotype attractors in such networks, where the status of some of the variables is fixed to active/inactive, while the others can have an arbitrary status, including ambiguous.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Commuting upper triangular binary morphisms</title>
      <description><![CDATA[A morphism $g$ from the free monoid $X^*$ into itself is called upper triangular if the matrix of $g$ is upper triangular. We characterize all upper triangular binary morphisms $g_1$ and $g_2$ such that $g_1g_2=g_2g_1$.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:28:13 +0000</pubDate>
      <link>https://fi.episciences.org/13931</link>
      <guid>https://fi.episciences.org/13931</guid>
      <author>Honkala, Juha</author>
      <dc:creator>Honkala, Juha</dc:creator>
      <content:encoded><![CDATA[A morphism $g$ from the free monoid $X^*$ into itself is called upper triangular if the matrix of $g$ is upper triangular. We characterize all upper triangular binary morphisms $g_1$ and $g_2$ such that $g_1g_2=g_2g_1$.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Decision Problems on Copying and Shuffling</title>
      <description><![CDATA[We study decision problems of the form: given a regular or linear context-free language $L$, is there a word of a given fixed form in $L$, where given fixed forms are based on word operations copy, marked copy, shuffle and their combinations.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:12:52 +0000</pubDate>
      <link>https://fi.episciences.org/13940</link>
      <guid>https://fi.episciences.org/13940</guid>
      <author>Halava, Vesa</author>
      <author>Harju, Tero</author>
      <author>Nowotka, Dirk</author>
      <author>Sahla, Esa</author>
      <dc:creator>Halava, Vesa</dc:creator>
      <dc:creator>Harju, Tero</dc:creator>
      <dc:creator>Nowotka, Dirk</dc:creator>
      <dc:creator>Sahla, Esa</dc:creator>
      <content:encoded><![CDATA[We study decision problems of the form: given a regular or linear context-free language $L$, is there a word of a given fixed form in $L$, where given fixed forms are based on word operations copy, marked copy, shuffle and their combinations.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Nonatomic Non-Cooperative Neighbourhood Balancing Games</title>
      <description><![CDATA[We introduce a game where players selfishly choose a resource and endure a cost depending on the number of players choosing nearby resources. We model the influences among resources by a weighted graph, directed or not. These games are generalizations of well-known games like Wardrop and congestion games. We study the conditions of equilibria existence and their efficiency if they exist. We conclude with studies of games whose influences among resources can be modelled by simple graphs.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:11:59 +0000</pubDate>
      <link>https://fi.episciences.org/12555</link>
      <guid>https://fi.episciences.org/12555</guid>
      <author>Auger, David</author>
      <author>Cohen, Johanne</author>
      <author>Lobstein, Antoine</author>
      <dc:creator>Auger, David</dc:creator>
      <dc:creator>Cohen, Johanne</dc:creator>
      <dc:creator>Lobstein, Antoine</dc:creator>
      <content:encoded><![CDATA[We introduce a game where players selfishly choose a resource and endure a cost depending on the number of players choosing nearby resources. We model the influences among resources by a weighted graph, directed or not. These games are generalizations of well-known games like Wardrop and congestion games. We study the conditions of equilibria existence and their efficiency if they exist. We conclude with studies of games whose influences among resources can be modelled by simple graphs.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Descriptional Complexity of Finite Automata -- Selected Highlights</title>
      <description><![CDATA[The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most studied state complexity questions deal with size comparisons of nondeterministic finite automata of differing degree of ambiguity. More generally, if for a regular language we compare the size of description by a finite automaton and by a more powerful language definition mechanism, such as a context-free grammar, we encounter non-recursive trade-offs. Operational state complexity studies the state complexity of the language resulting from a regularity preserving operation as a function of the complexity of the argument languages. Determining the state complexity of combined operations is generally challenging and for general combinations of operations that include intersection and marked concatenation it is uncomputable.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:10:50 +0000</pubDate>
      <link>https://fi.episciences.org/11559</link>
      <guid>https://fi.episciences.org/11559</guid>
      <author>Salomaa, Arto</author>
      <author>Salomaa, Kai</author>
      <author>Smith, Taylor J.</author>
      <dc:creator>Salomaa, Arto</dc:creator>
      <dc:creator>Salomaa, Kai</dc:creator>
      <dc:creator>Smith, Taylor J.</dc:creator>
      <content:encoded><![CDATA[The state complexity, respectively, nondeterministic state complexity of a regular language $L$ is the number of states of the minimal deterministic, respectively, of a minimal nondeterministic finite automaton for $L$. Some of the most studied state complexity questions deal with size comparisons of nondeterministic finite automata of differing degree of ambiguity. More generally, if for a regular language we compare the size of description by a finite automaton and by a more powerful language definition mechanism, such as a context-free grammar, we encounter non-recursive trade-offs. Operational state complexity studies the state complexity of the language resulting from a regularity preserving operation as a function of the complexity of the argument languages. Determining the state complexity of combined operations is generally challenging and for general combinations of operations that include intersection and marked concatenation it is uncomputable.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On three domination-based identification problems in block graphs</title>
      <description><![CDATA[The problems of determining the minimum-sized \emph{identifying}, \emph{locating-dominating} and \emph{open locating-dominating codes} of an input graph are special search problems that are challenging from both theoretical and computational viewpoints. In these problems, one selects a dominating set $C$ of a graph $G$ such that the vertices of a chosen subset of $V(G)$ (i.e. either $V(G)\setminus C$ or $V(G)$ itself) are uniquely determined by their neighborhoods in $C$. A typical line of attack for these problems is to determine tight bounds for the minimum codes in various graphs classes. In this work, we present tight lower and upper bounds for all three types of codes for \emph{block graphs} (i.e. diamond-free chordal graphs). Our bounds are in terms of the number of maximal cliques (or \emph{blocks}) of a block graph and the order of the graph. Two of our upper bounds verify conjectures from the literature - with one of them being now proven for block graphs in this article. As for the lower bounds, we prove them to be linear in terms of both the number of blocks and the order of the block graph. We provide examples of families of block graphs whose minimum codes attain these bounds, thus showing each bound to be tight.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:09:50 +0000</pubDate>
      <link>https://fi.episciences.org/13888</link>
      <guid>https://fi.episciences.org/13888</guid>
      <author>Chakraborty, Dipayan</author>
      <author>Foucaud, Florent</author>
      <author>Parreau, Aline</author>
      <author>Wagler, Annegret K.</author>
      <dc:creator>Chakraborty, Dipayan</dc:creator>
      <dc:creator>Foucaud, Florent</dc:creator>
      <dc:creator>Parreau, Aline</dc:creator>
      <dc:creator>Wagler, Annegret K.</dc:creator>
      <content:encoded><![CDATA[The problems of determining the minimum-sized \emph{identifying}, \emph{locating-dominating} and \emph{open locating-dominating codes} of an input graph are special search problems that are challenging from both theoretical and computational viewpoints. In these problems, one selects a dominating set $C$ of a graph $G$ such that the vertices of a chosen subset of $V(G)$ (i.e. either $V(G)\setminus C$ or $V(G)$ itself) are uniquely determined by their neighborhoods in $C$. A typical line of attack for these problems is to determine tight bounds for the minimum codes in various graphs classes. In this work, we present tight lower and upper bounds for all three types of codes for \emph{block graphs} (i.e. diamond-free chordal graphs). Our bounds are in terms of the number of maximal cliques (or \emph{blocks}) of a block graph and the order of the graph. Two of our upper bounds verify conjectures from the literature - with one of them being now proven for block graphs in this article. As for the lower bounds, we prove them to be linear in terms of both the number of blocks and the order of the block graph. We provide examples of families of block graphs whose minimum codes attain these bounds, thus showing each bound to be tight.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On Iiro Honkala's contributions to identifying codes</title>
      <description><![CDATA[A set $C$ of vertices in a graph $G=(V,E)$ is an identifying code if it is dominating and any two vertices of $V$ are dominated by distinct sets of codewords. This paper presents a survey of Iiro Honkala's contributions to the study of identifying codes with respect to several aspects: complexity of computing an identifying code, combinatorics in binary Hamming spaces, infinite grids, relationships between identifying codes and usual parameters in graphs, structural properties of graphs admitting identifying codes, and number of optimal identifying codes.]]></description>
      <pubDate>Sun, 10 Nov 2024 10:09:11 +0000</pubDate>
      <link>https://fi.episciences.org/13882</link>
      <guid>https://fi.episciences.org/13882</guid>
      <author>Hudry, Olivier</author>
      <author>Junnila, Ville</author>
      <author>Lobstein, Antoine</author>
      <dc:creator>Hudry, Olivier</dc:creator>
      <dc:creator>Junnila, Ville</dc:creator>
      <dc:creator>Lobstein, Antoine</dc:creator>
      <content:encoded><![CDATA[A set $C$ of vertices in a graph $G=(V,E)$ is an identifying code if it is dominating and any two vertices of $V$ are dominated by distinct sets of codewords. This paper presents a survey of Iiro Honkala's contributions to the study of identifying codes with respect to several aspects: complexity of computing an identifying code, combinatorics in binary Hamming spaces, infinite grids, relationships between identifying codes and usual parameters in graphs, structural properties of graphs admitting identifying codes, and number of optimal identifying codes.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On the Complexity of Proving Polyhedral Reductions</title>
      <description><![CDATA[We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer constraints between the marking of places. In addition to defining an automated proof method, this paper aims to better characterize polyhedral reductions, and to give an overview of their application to reachability problems. Our approach relies on encoding the equivalence problem into a set of SMT formulas whose satisfaction implies that the equivalence holds. The difficulty, in this context, arises from the fact that we need to handle infinite-state systems. For completeness, we exploit a connection with a class of Petri nets, called flat nets, that have Presburger-definable reachability sets. We have implemented our procedure, and we illustrate its use on several examples.]]></description>
      <pubDate>Sun, 10 Nov 2024 09:35:48 +0000</pubDate>
      <link>https://fi.episciences.org/14248</link>
      <guid>https://fi.episciences.org/14248</guid>
      <author>Amat, Nicolas</author>
      <author>Zilio, Silvano Dal</author>
      <author>Botlan, Didier Le</author>
      <dc:creator>Amat, Nicolas</dc:creator>
      <dc:creator>Zilio, Silvano Dal</dc:creator>
      <dc:creator>Botlan, Didier Le</dc:creator>
      <content:encoded><![CDATA[We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer constraints between the marking of places. In addition to defining an automated proof method, this paper aims to better characterize polyhedral reductions, and to give an overview of their application to reachability problems. Our approach relies on encoding the equivalence problem into a set of SMT formulas whose satisfaction implies that the equivalence holds. The difficulty, in this context, arises from the fact that we need to handle infinite-state systems. For completeness, we exploit a connection with a class of Petri nets, called flat nets, that have Presburger-definable reachability sets. We have implemented our procedure, and we illustrate its use on several examples.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Taking Complete Finite Prefixes To High Level, Symbolically</title>
      <description><![CDATA[Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of a P/T Petri net's unfolding contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. We evaluate this extended algorithm through a prototype implementation on four novel benchmark families. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net.]]></description>
      <pubDate>Sun, 10 Nov 2024 09:35:09 +0000</pubDate>
      <link>https://fi.episciences.org/14249</link>
      <guid>https://fi.episciences.org/14249</guid>
      <author>Würdemann, Nick</author>
      <author>Chatain, Thomas</author>
      <author>Haar, Stefan</author>
      <author>Panneke, Lukas</author>
      <dc:creator>Würdemann, Nick</dc:creator>
      <dc:creator>Chatain, Thomas</dc:creator>
      <dc:creator>Haar, Stefan</dc:creator>
      <dc:creator>Panneke, Lukas</dc:creator>
      <content:encoded><![CDATA[Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of a P/T Petri net's unfolding contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. We evaluate this extended algorithm through a prototype implementation on four novel benchmark families. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Myhill-Nerode Theorem for Higher-Dimensional Automata</title>
      <description><![CDATA[We establish a Myhill-Nerode type theorem for higher-dimensional automata (HDAs), stating that a language is regular if and only if it has finite prefix quotient. HDAs extend standard automata with additional structure, making it possible to distinguish between interleavings and concurrency. We also introduce deterministic HDAs and show that not all HDAs are determinizable, that is, there exist regular languages that cannot be recognised by a deterministic HDA. Using our theorem, we develop an internal characterisation of deterministic languages. Lastly, we develop analogues of the Myhill-Nerode construction and of determinacy for HDAs with interfaces.]]></description>
      <pubDate>Sun, 10 Nov 2024 09:34:00 +0000</pubDate>
      <link>https://fi.episciences.org/14246</link>
      <guid>https://fi.episciences.org/14246</guid>
      <author>Fahrenberg, Uli</author>
      <author>Ziemiański, Krzysztof</author>
      <dc:creator>Fahrenberg, Uli</dc:creator>
      <dc:creator>Ziemiański, Krzysztof</dc:creator>
      <content:encoded><![CDATA[We establish a Myhill-Nerode type theorem for higher-dimensional automata (HDAs), stating that a language is regular if and only if it has finite prefix quotient. HDAs extend standard automata with additional structure, making it possible to distinguish between interleavings and concurrency. We also introduce deterministic HDAs and show that not all HDAs are determinizable, that is, there exist regular languages that cannot be recognised by a deterministic HDA. Using our theorem, we develop an internal characterisation of deterministic languages. Lastly, we develop analogues of the Myhill-Nerode construction and of determinacy for HDAs with interfaces.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A rewriting-logic-with-SMT-based formal analysis and parameter synthesis framework for parametric time Petri nets</title>
      <description><![CDATA[This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the "standard" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude -- including full LTL model checking, analysis with user-defined analysis strategies, and even statistical model checking -- for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Romeo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Romeo in many cases.]]></description>
      <pubDate>Sat, 09 Nov 2024 23:00:00 +0000</pubDate>
      <link>https://fi.episciences.org/14251</link>
      <guid>https://fi.episciences.org/14251</guid>
      <author>Arias, Jaime</author>
      <author>Bae, Kyungmin</author>
      <author>Olarte, Carlos</author>
      <author>Ölveczky, Peter Csaba</author>
      <author>Petrucci, Laure</author>
      <dc:creator>Arias, Jaime</dc:creator>
      <dc:creator>Bae, Kyungmin</dc:creator>
      <dc:creator>Olarte, Carlos</dc:creator>
      <dc:creator>Ölveczky, Peter Csaba</dc:creator>
      <dc:creator>Petrucci, Laure</dc:creator>
      <content:encoded><![CDATA[This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the "standard" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude -- including full LTL model checking, analysis with user-defined analysis strategies, and even statistical model checking -- for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Romeo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Romeo in many cases.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Perturbation results for distance-edge-monitoring numbers</title>
      <description><![CDATA[Foucaud et al. recently introduced and initiated the study of a new graph-theoretic concept in the area of network monitoring. Given a graph $G=(V(G), E(G))$, a set $M \subseteq V(G)$ is a distance-edge-monitoring set if for every edge $e \in E(G)$, there is a vertex $x \in M$ and a vertex $y \in V(G)$ such that the edge $e$ belongs to all shortest paths between $x$ and $y$. The smallest size of such a set in $G$ is denoted by $\operatorname{dem}(G)$. Denoted by $G-e$ (resp. $G \backslash u$) the subgraph of $G$ obtained by removing the edge $e$ from $G$ (resp. a vertex $u$ together with all its incident edges from $G$). In this paper, we first show that $\operatorname{dem}(G-e)- \operatorname{dem}(G)\leq 2$ for any graph $G$ and edge $e \in E(G)$. Moreover, the bound is sharp. Next, we construct two graphs $G$ and $H$ to show that $\operatorname{dem}(G)-\operatorname{dem}(G\setminus u)$ and $\operatorname{dem}(H\setminus v)-\operatorname{dem}(H)$ can be arbitrarily large, where $u \in V(G)$ and $v \in V(H)$. We also study the relation between $\operatorname{dem}(H)$ and $\operatorname{dem}(G)$, where $H$ is a subgraph of $G$. In the end, we give an algorithm to judge whether the distance-edge monitoring set still remain in the resulting graph when any edge of the graph $G$ is deleted.]]></description>
      <pubDate>Mon, 08 Jul 2024 12:57:17 +0000</pubDate>
      <link>https://fi.episciences.org/13573</link>
      <guid>https://fi.episciences.org/13573</guid>
      <author>Yang, Chenxu</author>
      <author>Klasing, Ralf</author>
      <author>He, Changxiang</author>
      <author>Mao, Yaping</author>
      <dc:creator>Yang, Chenxu</dc:creator>
      <dc:creator>Klasing, Ralf</dc:creator>
      <dc:creator>He, Changxiang</dc:creator>
      <dc:creator>Mao, Yaping</dc:creator>
      <content:encoded><![CDATA[Foucaud et al. recently introduced and initiated the study of a new graph-theoretic concept in the area of network monitoring. Given a graph $G=(V(G), E(G))$, a set $M \subseteq V(G)$ is a distance-edge-monitoring set if for every edge $e \in E(G)$, there is a vertex $x \in M$ and a vertex $y \in V(G)$ such that the edge $e$ belongs to all shortest paths between $x$ and $y$. The smallest size of such a set in $G$ is denoted by $\operatorname{dem}(G)$. Denoted by $G-e$ (resp. $G \backslash u$) the subgraph of $G$ obtained by removing the edge $e$ from $G$ (resp. a vertex $u$ together with all its incident edges from $G$). In this paper, we first show that $\operatorname{dem}(G-e)- \operatorname{dem}(G)\leq 2$ for any graph $G$ and edge $e \in E(G)$. Moreover, the bound is sharp. Next, we construct two graphs $G$ and $H$ to show that $\operatorname{dem}(G)-\operatorname{dem}(G\setminus u)$ and $\operatorname{dem}(H\setminus v)-\operatorname{dem}(H)$ can be arbitrarily large, where $u \in V(G)$ and $v \in V(H)$. We also study the relation between $\operatorname{dem}(H)$ and $\operatorname{dem}(G)$, where $H$ is a subgraph of $G$. In the end, we give an algorithm to judge whether the distance-edge monitoring set still remain in the resulting graph when any edge of the graph $G$ is deleted.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Elimination distance to bounded degree on planar graphs</title>
      <description><![CDATA[We study the graph parameter elimination distance to bounded degree, which was introduced by Bulian and Dawar in their study of the parameterized complexity of the graph isomorphism problem. We prove that the problem is fixed-parameter tractable on planar graphs, that is, there exists an algorithm that given a planar graph $G$ and integers $d$ and $k$ decides in time $f(k,d)\cdot n^c$ for a computable function~$f$ and constant $c$ whether the elimination distance of $G$ to the class of degree $d$ graphs is at most $k$.]]></description>
      <pubDate>Mon, 08 Jul 2024 12:56:53 +0000</pubDate>
      <link>https://fi.episciences.org/13665</link>
      <guid>https://fi.episciences.org/13665</guid>
      <author>Lindermayr, Alexander</author>
      <author>Siebertz, Sebastian</author>
      <author>Vigny, Alexandre</author>
      <dc:creator>Lindermayr, Alexander</dc:creator>
      <dc:creator>Siebertz, Sebastian</dc:creator>
      <dc:creator>Vigny, Alexandre</dc:creator>
      <content:encoded><![CDATA[We study the graph parameter elimination distance to bounded degree, which was introduced by Bulian and Dawar in their study of the parameterized complexity of the graph isomorphism problem. We prove that the problem is fixed-parameter tractable on planar graphs, that is, there exists an algorithm that given a planar graph $G$ and integers $d$ and $k$ decides in time $f(k,d)\cdot n^c$ for a computable function~$f$ and constant $c$ whether the elimination distance of $G$ to the class of degree $d$ graphs is at most $k$.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Closeness and Residual Closeness of Harary Graphs</title>
      <description><![CDATA[Analysis of a network in terms of vulnerability is one of the most significant problems. Graph theory serves as a valuable tool for solving complex network problems, and there exist numerous graph-theoretic parameters to analyze the system's stability. Among these parameters, the closeness parameter stands out as one of the most commonly used vulnerability metrics. Its definition has evolved to enhance the ease of formulation and applicability to disconnected structures. Furthermore, based on the closeness parameter, vertex residual closeness, which is a newer and more sensitive parameter compared to other existing parameters, has been introduced as a new graph vulnerability index by Dangalchev. In this study, the outcomes of the closeness and vertex residual closeness parameters in Harary Graphs have been examined. Harary Graphs are well-known constructs that are distinguished by having $n$ vertices that are $k$-connected with the least possible number of edges.]]></description>
      <pubDate>Mon, 08 Jul 2024 12:56:26 +0000</pubDate>
      <link>https://fi.episciences.org/13618</link>
      <guid>https://fi.episciences.org/13618</guid>
      <author>Golpek, Hande Tuncel</author>
      <author>Aytac, Aysun</author>
      <dc:creator>Golpek, Hande Tuncel</dc:creator>
      <dc:creator>Aytac, Aysun</dc:creator>
      <content:encoded><![CDATA[Analysis of a network in terms of vulnerability is one of the most significant problems. Graph theory serves as a valuable tool for solving complex network problems, and there exist numerous graph-theoretic parameters to analyze the system's stability. Among these parameters, the closeness parameter stands out as one of the most commonly used vulnerability metrics. Its definition has evolved to enhance the ease of formulation and applicability to disconnected structures. Furthermore, based on the closeness parameter, vertex residual closeness, which is a newer and more sensitive parameter compared to other existing parameters, has been introduced as a new graph vulnerability index by Dangalchev. In this study, the outcomes of the closeness and vertex residual closeness parameters in Harary Graphs have been examined. Harary Graphs are well-known constructs that are distinguished by having $n$ vertices that are $k$-connected with the least possible number of edges.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On Rotation Distance of Rank Bounded Trees</title>
      <description><![CDATA[Computing the rotation distance between two binary trees with $n$ internal nodes efficiently (in $poly(n)$ time) is a long standing open question in the study of height balancing in tree data structures. In this paper, we initiate the study of this problem bounding the rank of the trees given at the input (defined by Ehrenfeucht and Haussler (1989) in the context of decision trees). We define the rank-bounded rotation distance between two given binary trees $T_1$ and $T_2$ (with $n$ internal nodes) of rank at most $r$, denoted by $d_r(T_1,T_2)$, as the length of the shortest sequence of rotations that transforms $T_1$ to $T_2$ with the restriction that the intermediate trees must be of rank at most $r$. We show that the rotation distance problem reduces in polynomial time to the rank bounded rotation distance problem. This motivates the study of the problem in the combinatorial and algorithmic frontiers. Observing that trees with rank $1$ coincide exactly with skew trees (binary trees where every internal node has at least one leaf as a child), we show the following results in this frontier : We present an $O(n^2)$ time algorithm for computing $d_1(T_1,T_2)$. That is, when the given trees are skew trees (we call this variant as skew rotation distance problem) - where the intermediate trees are restricted to be skew as well. In particular, our techniques imply that for any two skew trees $d(T_1,T_2) \le n^2$. We show the following upper bound : for any two trees $T_1$ and $T_2$ of rank at most $r_1$ and $r_2$ respectively, we have that: $d_r(T_1,T_2) \le n^2 (1+(2n+1)(r_1+r_2-2))$ where $r = max\{r_1,r_2\}$. This bound is asymptotically tight for $r=1$. En route our proof of the above theorems, we associate binary trees to permutations and bivariate polynomials, and prove several characterizations in the case of skew trees.]]></description>
      <pubDate>Mon, 08 Jul 2024 12:55:54 +0000</pubDate>
      <link>https://fi.episciences.org/13643</link>
      <guid>https://fi.episciences.org/13643</guid>
      <author>M., Anoop S. K.</author>
      <author>Sarma, Jayalal</author>
      <dc:creator>M., Anoop S. K.</dc:creator>
      <dc:creator>Sarma, Jayalal</dc:creator>
      <content:encoded><![CDATA[Computing the rotation distance between two binary trees with $n$ internal nodes efficiently (in $poly(n)$ time) is a long standing open question in the study of height balancing in tree data structures. In this paper, we initiate the study of this problem bounding the rank of the trees given at the input (defined by Ehrenfeucht and Haussler (1989) in the context of decision trees). We define the rank-bounded rotation distance between two given binary trees $T_1$ and $T_2$ (with $n$ internal nodes) of rank at most $r$, denoted by $d_r(T_1,T_2)$, as the length of the shortest sequence of rotations that transforms $T_1$ to $T_2$ with the restriction that the intermediate trees must be of rank at most $r$. We show that the rotation distance problem reduces in polynomial time to the rank bounded rotation distance problem. This motivates the study of the problem in the combinatorial and algorithmic frontiers. Observing that trees with rank $1$ coincide exactly with skew trees (binary trees where every internal node has at least one leaf as a child), we show the following results in this frontier : We present an $O(n^2)$ time algorithm for computing $d_1(T_1,T_2)$. That is, when the given trees are skew trees (we call this variant as skew rotation distance problem) - where the intermediate trees are restricted to be skew as well. In particular, our techniques imply that for any two skew trees $d(T_1,T_2) \le n^2$. We show the following upper bound : for any two trees $T_1$ and $T_2$ of rank at most $r_1$ and $r_2$ respectively, we have that: $d_r(T_1,T_2) \le n^2 (1+(2n+1)(r_1+r_2-2))$ where $r = max\{r_1,r_2\}$. This bound is asymptotically tight for $r=1$. En route our proof of the above theorems, we associate binary trees to permutations and bivariate polynomials, and prove several characterizations in the case of skew trees.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A strong Gram classification of non-negative unit forms of Dynkin type A</title>
      <description><![CDATA[An integral quadratic form q is usually identified with a bilinear form b such that its Gram matrix with respect to the canonical basis is upper triangular. Two integral quadratic forms are called strongly (resp. weakly) Gram congruent if their corresponding upper triangular bilinear forms (resp. their symmetrizations) are equivalent. If q is unitary, such upper triangular bilinear form is unimodular, and one considers the associated Coxeter transformation and its characteristic polynomial, the so-called Coxeter polynomial of q with this identification. Two strongly Gram congruent quadratic unit forms are weakly Gram congruent and have the same Coxeter polynomial. Here we show that the converse of this statement holds for the connected non-negative case of Dynkin type A_r and arbitrary corank, and use this characterization to complete a combinatorial classification of such quadratic forms started in [Fundamenta Informaticae 184(1):49-82, 2021] and [Fundamenta Informaticae 185(3):221-246, 2022].]]></description>
      <pubDate>Sat, 30 Mar 2024 11:13:13 +0000</pubDate>
      <link>https://fi.episciences.org/13099</link>
      <guid>https://fi.episciences.org/13099</guid>
      <author>Gonzalez, J. A. Jimenez</author>
      <dc:creator>Gonzalez, J. A. Jimenez</dc:creator>
      <content:encoded><![CDATA[An integral quadratic form q is usually identified with a bilinear form b such that its Gram matrix with respect to the canonical basis is upper triangular. Two integral quadratic forms are called strongly (resp. weakly) Gram congruent if their corresponding upper triangular bilinear forms (resp. their symmetrizations) are equivalent. If q is unitary, such upper triangular bilinear form is unimodular, and one considers the associated Coxeter transformation and its characteristic polynomial, the so-called Coxeter polynomial of q with this identification. Two strongly Gram congruent quadratic unit forms are weakly Gram congruent and have the same Coxeter polynomial. Here we show that the converse of this statement holds for the connected non-negative case of Dynkin type A_r and arbitrary corank, and use this characterization to complete a combinatorial classification of such quadratic forms started in [Fundamenta Informaticae 184(1):49-82, 2021] and [Fundamenta Informaticae 185(3):221-246, 2022].]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Two sufficient conditions for graphs to admit path factors</title>
      <description><![CDATA[Let $\mathcal{A}$ be a set of connected graphs. Then a spanning subgraph $A$ of $G$ is called an $\mathcal{A}$-factor if each component of $A$ is isomorphic to some member of $\mathcal{A}$. Especially, when every graph in $\mathcal{A}$ is a path, $A$ is a path factor. For a positive integer $d\geq2$, we write $\mathcal{P}_{\geq d}=\{P_i|i\geq d\}$. Then a $\mathcal{P}_{\geq d}$-factor means a path factor in which every component admits at least $d$ vertices. A graph $G$ is called a $(\mathcal{P}_{\geq d},m)$-factor deleted graph if $G-E'$ admits a $\mathcal{P}_{\geq d}$-factor for any $E'\subseteq E(G)$ with $|E'|=m$. A graph $G$ is called a $(\mathcal{P}_{\geq d},k)$-factor critical graph if $G-Q$ has a $\mathcal{P}_{\geq d}$-factor for any $Q\subseteq V(G)$ with $|Q|=k$. In this paper, we present two degree conditions for graphs to be $(\mathcal{P}_{\geq3},m)$-factor deleted graphs and $(\mathcal{P}_{\geq3},k)$-factor critical graphs. Furthermore, we show that the two results are best possible in some sense.]]></description>
      <pubDate>Sat, 30 Mar 2024 11:12:52 +0000</pubDate>
      <link>https://fi.episciences.org/13105</link>
      <guid>https://fi.episciences.org/13105</guid>
      <author>Zhou, Sizhong</author>
      <author>Wu, Jiancheng</author>
      <dc:creator>Zhou, Sizhong</dc:creator>
      <dc:creator>Wu, Jiancheng</dc:creator>
      <content:encoded><![CDATA[Let $\mathcal{A}$ be a set of connected graphs. Then a spanning subgraph $A$ of $G$ is called an $\mathcal{A}$-factor if each component of $A$ is isomorphic to some member of $\mathcal{A}$. Especially, when every graph in $\mathcal{A}$ is a path, $A$ is a path factor. For a positive integer $d\geq2$, we write $\mathcal{P}_{\geq d}=\{P_i|i\geq d\}$. Then a $\mathcal{P}_{\geq d}$-factor means a path factor in which every component admits at least $d$ vertices. A graph $G$ is called a $(\mathcal{P}_{\geq d},m)$-factor deleted graph if $G-E'$ admits a $\mathcal{P}_{\geq d}$-factor for any $E'\subseteq E(G)$ with $|E'|=m$. A graph $G$ is called a $(\mathcal{P}_{\geq d},k)$-factor critical graph if $G-Q$ has a $\mathcal{P}_{\geq d}$-factor for any $Q\subseteq V(G)$ with $|Q|=k$. In this paper, we present two degree conditions for graphs to be $(\mathcal{P}_{\geq3},m)$-factor deleted graphs and $(\mathcal{P}_{\geq3},k)$-factor critical graphs. Furthermore, we show that the two results are best possible in some sense.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Link Residual Closeness of Harary Graphs</title>
      <description><![CDATA[The study of networks characteristics is an important subject in different fields, like math, chemistry, transportation, social network analysis etc. The residual closeness is one of the most sensitive measure of graphs vulnerability. In this article we calculate the link residual closeness of Harary graphs.]]></description>
      <pubDate>Sat, 30 Mar 2024 11:12:26 +0000</pubDate>
      <link>https://fi.episciences.org/13126</link>
      <guid>https://fi.episciences.org/13126</guid>
      <author>Dangalchev, Ch.</author>
      <dc:creator>Dangalchev, Ch.</dc:creator>
      <content:encoded><![CDATA[The study of networks characteristics is an important subject in different fields, like math, chemistry, transportation, social network analysis etc. The residual closeness is one of the most sensitive measure of graphs vulnerability. In this article we calculate the link residual closeness of Harary graphs.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Correctness Notions for Petri Nets with Identifiers</title>
      <description><![CDATA[A model of an information system describes its processes and how resources are involved in these processes to manipulate data objects. This paper presents an extension to the Petri nets formalism suitable for describing information systems in which states refer to object instances of predefined types and resources are identified as instances of special object types. Several correctness criteria for resource- and object-aware information systems models are proposed, supplemented with discussions on their decidability for interesting classes of systems. These new correctness criteria can be seen as generalizations of the classical soundness property of workflow models concerned with process control flow correctness.]]></description>
      <pubDate>Mon, 12 Feb 2024 15:24:23 +0000</pubDate>
      <link>https://fi.episciences.org/12902</link>
      <guid>https://fi.episciences.org/12902</guid>
      <author>van der Werf, Jan Martijn E. M.</author>
      <author>Rivkin, Andrey</author>
      <author>Montali, Marco</author>
      <author>Polyvyanyy, Artem</author>
      <dc:creator>van der Werf, Jan Martijn E. M.</dc:creator>
      <dc:creator>Rivkin, Andrey</dc:creator>
      <dc:creator>Montali, Marco</dc:creator>
      <dc:creator>Polyvyanyy, Artem</dc:creator>
      <content:encoded><![CDATA[A model of an information system describes its processes and how resources are involved in these processes to manipulate data objects. This paper presents an extension to the Petri nets formalism suitable for describing information systems in which states refer to object instances of predefined types and resources are identified as instances of special object types. Several correctness criteria for resource- and object-aware information systems models are proposed, supplemented with discussions on their decidability for interesting classes of systems. These new correctness criteria can be seen as generalizations of the classical soundness property of workflow models concerned with process control flow correctness.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Discovering Process Models With Long-Term Dependencies While Providing Guarantees and Filtering Infrequent Behavior Patterns</title>
      <description><![CDATA[In process discovery, the goal is to find, for a given event log, the model describing the underlying process. While process models can be represented in a variety of ways, Petri nets form a theoretically well-explored description language and are therefore often used. In this paper, we extend the eST-Miner process discovery algorithm. The eST-Miner computes a set of Petri net places which are considered to be fitting with respect to a certain fraction of the behavior described by the given event log as indicated by a given noise threshold. It evaluates all possible candidate places using token-based replay. The set of replayable traces is determined for each place in isolation, i.e., these sets do not need to be consistent. This allows the algorithm to abstract from infrequent behavioral patterns occurring only in some traces. However, when combining places into a Petri net by connecting them to the corresponding uniquely labeled transitions, the resulting net can replay exactly those traces from the event log that are allowed by the combination of all inserted places. Thus, inserting places one-by-one without considering their combined effect may result in deadlocks and low fitness of the Petri net. In this paper, we explore adaptions of the eST-Miner, that aim to select a subset of places such that the resulting Petri net guarantees a definable minimal fitness while maintaining high precision with respect to the input event log. Furthermore, current place evaluation techniques tend to block the execution of infrequent activity labels. Thus, a refined place fitness metric is introduced and thoroughly investigated. In our experiments we use real and artificial event logs to evaluate and compare the impact of the various place selection strategies and place fitness evaluation metrics on the returned Petri net.]]></description>
      <pubDate>Mon, 12 Feb 2024 15:23:52 +0000</pubDate>
      <link>https://fi.episciences.org/12952</link>
      <guid>https://fi.episciences.org/12952</guid>
      <author>Mannel, Lisa Luise</author>
      <author>van der Aalst, Wil M. P.</author>
      <dc:creator>Mannel, Lisa Luise</dc:creator>
      <dc:creator>van der Aalst, Wil M. P.</dc:creator>
      <content:encoded><![CDATA[In process discovery, the goal is to find, for a given event log, the model describing the underlying process. While process models can be represented in a variety of ways, Petri nets form a theoretically well-explored description language and are therefore often used. In this paper, we extend the eST-Miner process discovery algorithm. The eST-Miner computes a set of Petri net places which are considered to be fitting with respect to a certain fraction of the behavior described by the given event log as indicated by a given noise threshold. It evaluates all possible candidate places using token-based replay. The set of replayable traces is determined for each place in isolation, i.e., these sets do not need to be consistent. This allows the algorithm to abstract from infrequent behavioral patterns occurring only in some traces. However, when combining places into a Petri net by connecting them to the corresponding uniquely labeled transitions, the resulting net can replay exactly those traces from the event log that are allowed by the combination of all inserted places. Thus, inserting places one-by-one without considering their combined effect may result in deadlocks and low fitness of the Petri net. In this paper, we explore adaptions of the eST-Miner, that aim to select a subset of places such that the resulting Petri net guarantees a definable minimal fitness while maintaining high precision with respect to the input event log. Furthermore, current place evaluation techniques tend to block the execution of infrequent activity labels. Thus, a refined place fitness metric is introduced and thoroughly investigated. In our experiments we use real and artificial event logs to evaluate and compare the impact of the various place selection strategies and place fitness evaluation metrics on the returned Petri net.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Waiting Nets: State Classes and Taxonomy</title>
      <description><![CDATA[In time Petri nets (TPNs), time and control are tightly connected: time measurement for a transition starts only when all resources needed to fire it are available. Further, upper bounds on duration of enabledness can force transitions to fire (this is called urgency). For many systems, one wants to decouple control and time, i.e. start measuring time as soon as a part of the preset of a transition is filled, and fire it after some delay \underline{and} when all needed resources are available. This paper considers an extension of TPN called waiting nets that dissociates time measurement and control. Their semantics allows time measurement to start with incomplete presets, and can ignore urgency when upper bounds of intervals are reached but all resources needed to fire are not yet available. Firing of a transition is then allowed as soon as missing resources are available. It is known that extending bounded TPNs with stopwatches leads to undecidability. Our extension is weaker, and we show how to compute a finite state class graph for bounded waiting nets, yielding decidability of reachability and coverability. We then compare expressiveness of waiting nets with that of other models w.r.t. timed language equivalence, and show that they are strictly more expressive than TPNs.]]></description>
      <pubDate>Mon, 12 Feb 2024 15:23:21 +0000</pubDate>
      <link>https://fi.episciences.org/12953</link>
      <guid>https://fi.episciences.org/12953</guid>
      <author>Hélouët, Loïc</author>
      <author>Agrawal, Pranay</author>
      <dc:creator>Hélouët, Loïc</dc:creator>
      <dc:creator>Agrawal, Pranay</dc:creator>
      <content:encoded><![CDATA[In time Petri nets (TPNs), time and control are tightly connected: time measurement for a transition starts only when all resources needed to fire it are available. Further, upper bounds on duration of enabledness can force transitions to fire (this is called urgency). For many systems, one wants to decouple control and time, i.e. start measuring time as soon as a part of the preset of a transition is filled, and fire it after some delay \underline{and} when all needed resources are available. This paper considers an extension of TPN called waiting nets that dissociates time measurement and control. Their semantics allows time measurement to start with incomplete presets, and can ignore urgency when upper bounds of intervals are reached but all resources needed to fire are not yet available. Firing of a transition is then allowed as soon as missing resources are available. It is known that extending bounded TPNs with stopwatches leads to undecidability. Our extension is weaker, and we show how to compute a finite state class graph for bounded waiting nets, yielding decidability of reachability and coverability. We then compare expressiveness of waiting nets with that of other models w.r.t. timed language equivalence, and show that they are strictly more expressive than TPNs.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Diameter of General Knödel Graphs</title>
      <description><![CDATA[The Kn\"odel graph $W_{\Delta,n}$ is a $\Delta$-regular bipartition graph on $n\ge 2^{\Delta}$ vertices and $n$ is an even integer. The vertices of $W_{\Delta,n}$ are the pairs $(i,j)$ with $i=1,2$ and $0\le j\le n/2-1$. For every $j$, $0\le j\le n/2-1$, there is an edge between vertex $(1, j)$ and every vertex $(2,(j+2^k-1) \mod (n/2))$, for $k=0,1,\cdots,\Delta-1$. In this paper we obtain some formulas for evaluating the distance of vertices of the Kn\"odel graph and by them, we provide the formula $diam(W_{\Delta,n})=1+\lceil\frac{n-2}{2^{\Delta}-2}\rceil$ for the diameter of $W_{\Delta,n}$, where $n\ge (2\Delta-5)(2^{\Delta}-2)+4$.]]></description>
      <pubDate>Sat, 14 Oct 2023 10:52:07 +0000</pubDate>
      <link>https://fi.episciences.org/12399</link>
      <guid>https://fi.episciences.org/12399</guid>
      <author>Musawi, Seyed Reza</author>
      <author>Kiashi, Esameil Nazari</author>
      <dc:creator>Musawi, Seyed Reza</dc:creator>
      <dc:creator>Kiashi, Esameil Nazari</dc:creator>
      <content:encoded><![CDATA[The Kn\"odel graph $W_{\Delta,n}$ is a $\Delta$-regular bipartition graph on $n\ge 2^{\Delta}$ vertices and $n$ is an even integer. The vertices of $W_{\Delta,n}$ are the pairs $(i,j)$ with $i=1,2$ and $0\le j\le n/2-1$. For every $j$, $0\le j\le n/2-1$, there is an edge between vertex $(1, j)$ and every vertex $(2,(j+2^k-1) \mod (n/2))$, for $k=0,1,\cdots,\Delta-1$. In this paper we obtain some formulas for evaluating the distance of vertices of the Kn\"odel graph and by them, we provide the formula $diam(W_{\Delta,n})=1+\lceil\frac{n-2}{2^{\Delta}-2}\rceil$ for the diameter of $W_{\Delta,n}$, where $n\ge (2\Delta-5)(2^{\Delta}-2)+4$.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>String Covering: A Survey</title>
      <description><![CDATA[The study of strings is an important combinatorial field that precedes the digital computer. Strings can be very long, trillions of letters, so it is important to find compact representations. Here we first survey various forms of one potential compaction methodology, the cover of a given string x, initially proposed in a simple form in 1990, but increasingly of interest as more sophisticated variants have been discovered. We then consider covering by a seed; that is, a cover of a superstring of x. We conclude with many proposals for research directions that could make significant contributions to string processing in future.]]></description>
      <pubDate>Sat, 14 Oct 2023 10:51:50 +0000</pubDate>
      <link>https://fi.episciences.org/12400</link>
      <guid>https://fi.episciences.org/12400</guid>
      <author>Mhaskar, Neerja</author>
      <author>Smyth, W. F.</author>
      <dc:creator>Mhaskar, Neerja</dc:creator>
      <dc:creator>Smyth, W. F.</dc:creator>
      <content:encoded><![CDATA[The study of strings is an important combinatorial field that precedes the digital computer. Strings can be very long, trillions of letters, so it is important to find compact representations. Here we first survey various forms of one potential compaction methodology, the cover of a given string x, initially proposed in a simple form in 1990, but increasingly of interest as more sophisticated variants have been discovered. We then consider covering by a seed; that is, a cover of a superstring of x. We conclude with many proposals for research directions that could make significant contributions to string processing in future.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Computing square roots in quaternion algebras</title>
      <description><![CDATA[We present an explicit algorithmic method for computing square roots in quaternion algebras over global fields of characteristic different from 2.]]></description>
      <pubDate>Sat, 14 Oct 2023 10:51:31 +0000</pubDate>
      <link>https://fi.episciences.org/12404</link>
      <guid>https://fi.episciences.org/12404</guid>
      <author>Koprowski, Przemysław</author>
      <dc:creator>Koprowski, Przemysław</dc:creator>
      <content:encoded><![CDATA[We present an explicit algorithmic method for computing square roots in quaternion algebras over global fields of characteristic different from 2.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Methods for Efficient Unfolding of Colored Petri Nets</title>
      <description><![CDATA[Colored Petri nets offer a compact and user friendly representation of the traditional P/T nets and colored nets with finite color ranges can be unfolded into the underlying P/T nets, however, at the expense of an exponential explosion in size. We present two novel techniques based on static analysis in order to reduce the size of unfolded colored nets. The first method identifies colors that behave equivalently and groups them into equivalence classes, potentially reducing the number of used colors. The second method overapproximates the sets of colors that can appear in places and excludes colors that can never be present in a given place. Both methods are complementary and the combined approach allows us to significantly reduce the size of multiple colored Petri nets from the Model Checking Contest benchmark. We compare the performance of our unfolder with state-of-the-art techniques implemented in the tools MCC, Spike and ITS-Tools, and while our approach is competitive w.r.t. unfolding time, it also outperforms the existing approaches both in the size of unfolded nets as well as in the number of answered model checking queries from the 2021 Model Checking Contest.]]></description>
      <pubDate>Sat, 14 Oct 2023 10:50:59 +0000</pubDate>
      <link>https://fi.episciences.org/12398</link>
      <guid>https://fi.episciences.org/12398</guid>
      <author>Bilgram, Alexander</author>
      <author>Jensen, Peter G.</author>
      <author>Pedersen, Thomas</author>
      <author>Srba, Jiri</author>
      <author>Taankvist, Peter H.</author>
      <dc:creator>Bilgram, Alexander</dc:creator>
      <dc:creator>Jensen, Peter G.</dc:creator>
      <dc:creator>Pedersen, Thomas</dc:creator>
      <dc:creator>Srba, Jiri</dc:creator>
      <dc:creator>Taankvist, Peter H.</dc:creator>
      <content:encoded><![CDATA[Colored Petri nets offer a compact and user friendly representation of the traditional P/T nets and colored nets with finite color ranges can be unfolded into the underlying P/T nets, however, at the expense of an exponential explosion in size. We present two novel techniques based on static analysis in order to reduce the size of unfolded colored nets. The first method identifies colors that behave equivalently and groups them into equivalence classes, potentially reducing the number of used colors. The second method overapproximates the sets of colors that can appear in places and excludes colors that can never be present in a given place. Both methods are complementary and the combined approach allows us to significantly reduce the size of multiple colored Petri nets from the Model Checking Contest benchmark. We compare the performance of our unfolder with state-of-the-art techniques implemented in the tools MCC, Spike and ITS-Tools, and while our approach is competitive w.r.t. unfolding time, it also outperforms the existing approaches both in the size of unfolded nets as well as in the number of answered model checking queries from the 2021 Model Checking Contest.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On the Complexity of Techniques That Make Transition Systems Implementable by Boolean Nets</title>
      <description><![CDATA[Synthesis consists in deciding whether a given labeled transition system (TS) $A$ can be implemented by a net $N$ of type $\tau$. In case of a negative decision, it may be possible to convert $A$ into an implementable TS $B$ by applying various modification techniques, like relabeling edges that previously had the same label, suppressing edges/states/events, etc. It may however be useful to limit the number of such modifications to stay close to the original problem, or optimize the technique. In this paper, we show that most of the corresponding problems are NP-complete if $\tau$ corresponds to the type of flip-flop nets or some flip-flop net derivatives.]]></description>
      <pubDate>Sat, 14 Oct 2023 10:50:39 +0000</pubDate>
      <link>https://fi.episciences.org/12403</link>
      <guid>https://fi.episciences.org/12403</guid>
      <author>Devillers, Raymond</author>
      <author>Tredup, Ronny</author>
      <dc:creator>Devillers, Raymond</dc:creator>
      <dc:creator>Tredup, Ronny</dc:creator>
      <content:encoded><![CDATA[Synthesis consists in deciding whether a given labeled transition system (TS) $A$ can be implemented by a net $N$ of type $\tau$. In case of a negative decision, it may be possible to convert $A$ into an implementable TS $B$ by applying various modification techniques, like relabeling edges that previously had the same label, suppressing edges/states/events, etc. It may however be useful to limit the number of such modifications to stay close to the original problem, or optimize the technique. In this paper, we show that most of the corresponding problems are NP-complete if $\tau$ corresponds to the type of flip-flop nets or some flip-flop net derivatives.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Reachability In Simple Neural Networks</title>
      <description><![CDATA[We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and specifications over the input/output dimension given by conjunctions of linear inequalities. We recapitulate the proof and repair some flaws in the original upper and lower bound proofs. Motivated by the general result, we show that NP-hardness already holds for restricted classes of simple specifications and neural networks. Allowing for a single hidden layer and an output dimension of one as well as neural networks with just one negative, zero and one positive weight or bias is sufficient to ensure NP-hardness. Additionally, we give a thorough discussion and outlook of possible extensions for this direction of research on neural network verification.]]></description>
      <pubDate>Sat, 14 Oct 2023 10:50:19 +0000</pubDate>
      <link>https://fi.episciences.org/12397</link>
      <guid>https://fi.episciences.org/12397</guid>
      <author>Sälzer, Marco</author>
      <author>Lange, Martin</author>
      <dc:creator>Sälzer, Marco</dc:creator>
      <dc:creator>Lange, Martin</dc:creator>
      <content:encoded><![CDATA[We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and specifications over the input/output dimension given by conjunctions of linear inequalities. We recapitulate the proof and repair some flaws in the original upper and lower bound proofs. Motivated by the general result, we show that NP-hardness already holds for restricted classes of simple specifications and neural networks. Allowing for a single hidden layer and an output dimension of one as well as neural networks with just one negative, zero and one positive weight or bias is sufficient to ensure NP-hardness. Additionally, we give a thorough discussion and outlook of possible extensions for this direction of research on neural network verification.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Absent Subsequences in Words</title>
      <description><![CDATA[An absent factor of a string $w$ is a string $u$ which does not occur as a contiguous substring (a.k.a. factor) inside $w$. We extend this well-studied notion and define absent subsequences: a string $u$ is an absent subsequence of a string $w$ if $u$ does not occur as subsequence (a.k.a. scattered factor) inside $w$. Of particular interest to us are minimal absent subsequences, i.e., absent subsequences whose every subsequence is not absent, and shortest absent subsequences, i.e., absent subsequences of minimal length. We show a series of combinatorial and algorithmic results regarding these two notions. For instance: we give combinatorial characterisations of the sets of minimal and, respectively, shortest absent subsequences in a word, as well as compact representations of these sets; we show how we can test efficiently if a string is a shortest or minimal absent subsequence in a word, and we give efficient algorithms computing the lexicographically smallest absent subsequence of each kind; also, we show how a data structure for answering shortest absent subsequence-queries for the factors of a given string can be efficiently computed.]]></description>
      <pubDate>Sat, 14 Oct 2023 10:49:52 +0000</pubDate>
      <link>https://fi.episciences.org/12396</link>
      <guid>https://fi.episciences.org/12396</guid>
      <author>Kosche, Maria</author>
      <author>Koß, Tore</author>
      <author>Manea, Florin</author>
      <author>Siemer, Stefan</author>
      <dc:creator>Kosche, Maria</dc:creator>
      <dc:creator>Koß, Tore</dc:creator>
      <dc:creator>Manea, Florin</dc:creator>
      <dc:creator>Siemer, Stefan</dc:creator>
      <content:encoded><![CDATA[An absent factor of a string $w$ is a string $u$ which does not occur as a contiguous substring (a.k.a. factor) inside $w$. We extend this well-studied notion and define absent subsequences: a string $u$ is an absent subsequence of a string $w$ if $u$ does not occur as subsequence (a.k.a. scattered factor) inside $w$. Of particular interest to us are minimal absent subsequences, i.e., absent subsequences whose every subsequence is not absent, and shortest absent subsequences, i.e., absent subsequences of minimal length. We show a series of combinatorial and algorithmic results regarding these two notions. For instance: we give combinatorial characterisations of the sets of minimal and, respectively, shortest absent subsequences in a word, as well as compact representations of these sets; we show how we can test efficiently if a string is a shortest or minimal absent subsequence in a word, and we give efficient algorithms computing the lexicographically smallest absent subsequence of each kind; also, we show how a data structure for answering shortest absent subsequence-queries for the factors of a given string can be efficiently computed.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Diffuse and Localized Functional Dysconnectivity in Schizophrenia: a Bootstrapped Top-Down Approach</title>
      <description><![CDATA[Schizophrenia (SZ) is a brain disorder leading to detached mind's normally integrated processes. Hence, the exploration of the symptoms in relation to functional connectivity (FC) had great relevance in the field. FC can be investigated on different levels, going from global features to single edges between regions, revealing diffuse and localized dysconnection patterns. In this context, SZ is characterized by a diverse global integration with reduced connectivity in specific areas of the Default Mode Network (DMN). However, the assessment of FC presents various sources of uncertainty. This study proposes a multi-level approach for more robust group-comparison. FC between 74 AAL brain areas of 15 healthy controls (HC) and 12 SZ subjects were used. Multi-level analyses and graph topological indexes evaluation were carried out by the previously published SPIDER-NET tool. Robustness was augmented by bootstrapped (BOOT) data and the stability was evaluated by removing one (RST1) or two subjects (RST2). The DMN subgraph was evaluated, toegether with overall local indexes and connection weights to enhance common activations/deactivations. At a global level, expected trends were found. The robustness assessment tests highlighted more stable results for BOOT compared to the direct data testing. Conversely, significant results were found in the analysis at lower levels. The DMN highlighted reduced connectivity and strength as well as increased deactivation in the SZ group. At local level, 13 areas were found to be significantly different ($p<0.05$), highlighting a greater divergence in the frontal lobe. These results were confirmed analyzing the negative edges, suggesting inverted connectivity between prefronto-temporal areas. In conclusion, multi-level analysis supported by BOOT is highly recommended, especially when diffuse and localized dysconnections must be investigated in limited samples.]]></description>
      <pubDate>Thu, 21 Sep 2023 08:49:25 +0000</pubDate>
      <link>https://fi.episciences.org/11610</link>
      <guid>https://fi.episciences.org/11610</guid>
      <author>Coluzzi, Davide</author>
      <author>Baselli, Giuseppe</author>
      <dc:creator>Coluzzi, Davide</dc:creator>
      <dc:creator>Baselli, Giuseppe</dc:creator>
      <content:encoded><![CDATA[Schizophrenia (SZ) is a brain disorder leading to detached mind's normally integrated processes. Hence, the exploration of the symptoms in relation to functional connectivity (FC) had great relevance in the field. FC can be investigated on different levels, going from global features to single edges between regions, revealing diffuse and localized dysconnection patterns. In this context, SZ is characterized by a diverse global integration with reduced connectivity in specific areas of the Default Mode Network (DMN). However, the assessment of FC presents various sources of uncertainty. This study proposes a multi-level approach for more robust group-comparison. FC between 74 AAL brain areas of 15 healthy controls (HC) and 12 SZ subjects were used. Multi-level analyses and graph topological indexes evaluation were carried out by the previously published SPIDER-NET tool. Robustness was augmented by bootstrapped (BOOT) data and the stability was evaluated by removing one (RST1) or two subjects (RST2). The DMN subgraph was evaluated, toegether with overall local indexes and connection weights to enhance common activations/deactivations. At a global level, expected trends were found. The robustness assessment tests highlighted more stable results for BOOT compared to the direct data testing. Conversely, significant results were found in the analysis at lower levels. The DMN highlighted reduced connectivity and strength as well as increased deactivation in the SZ group. At local level, 13 areas were found to be significantly different ($p<0.05$), highlighting a greater divergence in the frontal lobe. These results were confirmed analyzing the negative edges, suggesting inverted connectivity between prefronto-temporal areas. In conclusion, multi-level analysis supported by BOOT is highly recommended, especially when diffuse and localized dysconnections must be investigated in limited samples.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Error Correction for Discrete Tomography</title>
      <description><![CDATA[Discrete tomography focuses on the reconstruction of functions $f: A \to \mathbb{R}$ from their line sums in a finite number $d$ of directions, where $A$ is a finite subset of $\mathbb{Z}^2$. Consequently, the techniques of discrete tomography often find application in areas where only a small number of projections are available. In 1978 M.B. Katz gave a necessary and sufficient condition for the uniqueness of the solution. Since then, several reconstruction methods have been introduced. Recently Pagani and Tijdeman developed a fast method to reconstruct $f$ if it is uniquely determined. Subsequently Ceko, Pagani and Tijdeman extended the method to the reconstruction of a function with the same line sums of $f$ in the general case. Up to here we assumed that the line sums are exact. In this paper we investigate the case where a small number of line sums are incorrect as may happen when discrete tomography is applied for data storage or transmission. We show how less than $d/2$ errors can be corrected and that this bound is the best possible.]]></description>
      <pubDate>Thu, 21 Sep 2023 08:48:39 +0000</pubDate>
      <link>https://fi.episciences.org/11635</link>
      <guid>https://fi.episciences.org/11635</guid>
      <author>Ceko, M.</author>
      <author>Hajdu, L.</author>
      <author>Tijdeman, R.</author>
      <dc:creator>Ceko, M.</dc:creator>
      <dc:creator>Hajdu, L.</dc:creator>
      <dc:creator>Tijdeman, R.</dc:creator>
      <content:encoded><![CDATA[Discrete tomography focuses on the reconstruction of functions $f: A \to \mathbb{R}$ from their line sums in a finite number $d$ of directions, where $A$ is a finite subset of $\mathbb{Z}^2$. Consequently, the techniques of discrete tomography often find application in areas where only a small number of projections are available. In 1978 M.B. Katz gave a necessary and sufficient condition for the uniqueness of the solution. Since then, several reconstruction methods have been introduced. Recently Pagani and Tijdeman developed a fast method to reconstruct $f$ if it is uniquely determined. Subsequently Ceko, Pagani and Tijdeman extended the method to the reconstruction of a function with the same line sums of $f$ in the general case. Up to here we assumed that the line sums are exact. In this paper we investigate the case where a small number of line sums are incorrect as may happen when discrete tomography is applied for data storage or transmission. We show how less than $d/2$ errors can be corrected and that this bound is the best possible.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Reconstruction of Convex Sets from One or Two X-rays</title>
      <description><![CDATA[We consider a class of problems of Discrete Tomography which has been deeply investigated in the past: the reconstruction of convex lattice sets from their horizontal and/or vertical X-rays, i.e. from the number of points in a sequence of consecutive horizontal and vertical lines. The reconstruction of the HV-convex polyominoes works usually in two steps, first the filling step consisting in filling operations, second the convex aggregation of the switching components. We prove three results about the convex aggregation step: (1) The convex aggregation step used for the reconstruction of HV-convex polyominoes does not always provide a solution. The example yielding to this result is called \textit{the bad guy} and disproves a conjecture of the domain. (2) The reconstruction of a digital convex lattice set from only one X-ray can be performed in polynomial time. We prove it by encoding the convex aggregation problem in a Directed Acyclic Graph. (3) With the same strategy, we prove that the reconstruction of fat digital convex sets from their horizontal and vertical X-rays can be solved in polynomial time. Fatness is a property of the digital convex sets regarding the relative position of the left, right, top and bottom points of the set. The complexity of the reconstruction of the lattice sets which are not fat remains an open question.]]></description>
      <pubDate>Thu, 21 Sep 2023 08:48:21 +0000</pubDate>
      <link>https://fi.episciences.org/11642</link>
      <guid>https://fi.episciences.org/11642</guid>
      <author>Gerard, Yan</author>
      <dc:creator>Gerard, Yan</dc:creator>
      <content:encoded><![CDATA[We consider a class of problems of Discrete Tomography which has been deeply investigated in the past: the reconstruction of convex lattice sets from their horizontal and/or vertical X-rays, i.e. from the number of points in a sequence of consecutive horizontal and vertical lines. The reconstruction of the HV-convex polyominoes works usually in two steps, first the filling step consisting in filling operations, second the convex aggregation of the switching components. We prove three results about the convex aggregation step: (1) The convex aggregation step used for the reconstruction of HV-convex polyominoes does not always provide a solution. The example yielding to this result is called \textit{the bad guy} and disproves a conjecture of the domain. (2) The reconstruction of a digital convex lattice set from only one X-ray can be performed in polynomial time. We prove it by encoding the convex aggregation problem in a Directed Acyclic Graph. (3) With the same strategy, we prove that the reconstruction of fat digital convex sets from their horizontal and vertical X-rays can be solved in polynomial time. Fatness is a property of the digital convex sets regarding the relative position of the left, right, top and bottom points of the set. The complexity of the reconstruction of the lattice sets which are not fat remains an open question.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On taxicab distance mean functions and their geometric applications: methods, implementations and examples</title>
      <description><![CDATA[A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points the average distance is typically given by integration over the focal set. The paper contains a survey on the applications of taxicab distance mean functions and generalized conics' theory in geometric tomography: bisection of the focal set and reconstruction problems by coordinate X-rays. The theoretical results are illustrated by implementations in Maple, methods and examples as well.]]></description>
      <pubDate>Thu, 21 Sep 2023 08:47:50 +0000</pubDate>
      <link>https://fi.episciences.org/11651</link>
      <guid>https://fi.episciences.org/11651</guid>
      <author>Vincze, Csaba</author>
      <author>Nagy, Ábris</author>
      <dc:creator>Vincze, Csaba</dc:creator>
      <dc:creator>Nagy, Ábris</dc:creator>
      <content:encoded><![CDATA[A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points the average distance is typically given by integration over the focal set. The paper contains a survey on the applications of taxicab distance mean functions and generalized conics' theory in geometric tomography: bisection of the focal set and reconstruction problems by coordinate X-rays. The theoretical results are illustrated by implementations in Maple, methods and examples as well.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On Minimization and Learning of Deterministic $\omega$-Automata in the Presence of Don't Care Words</title>
      <description><![CDATA[We study minimization problems for deterministic $\omega$-automata in the presence of don't care words. We prove that the number of priorities in deterministic parity automata can be efficiently minimized under an arbitrary set of don't care words. We derive that from a more general result from which one also obtains an efficient minimization algorithm for deterministic parity automata with informative right-congruence (without don't care words). We then analyze languages of don't care words with a trivial right-congruence. For such sets of don't care words it is known that weak deterministic B\"uchi automata (WDBA) have a unique minimal automaton that can be efficiently computed from a given WDBA (Eisinger, Klaedtke 2006). We give a congruence-based characterization of the corresponding minimal WDBA, and show that the don't care minimization results for WDBA do not extend to deterministic $\omega$-automata with informative right-congruence: for this class there is no unique minimal automaton for a given don't care set with trivial right congruence, and the minimization problem is NP-hard. Finally, we extend an active learning algorithm for WDBA (Maler, Pnueli 1995) to the setting with an additional set of don't care words with trivial right-congruence.]]></description>
      <pubDate>Sat, 01 Jul 2023 09:54:31 +0000</pubDate>
      <link>https://fi.episciences.org/11460</link>
      <guid>https://fi.episciences.org/11460</guid>
      <author>Löding, Christof</author>
      <author>Stachon, Max Philip</author>
      <dc:creator>Löding, Christof</dc:creator>
      <dc:creator>Stachon, Max Philip</dc:creator>
      <content:encoded><![CDATA[We study minimization problems for deterministic $\omega$-automata in the presence of don't care words. We prove that the number of priorities in deterministic parity automata can be efficiently minimized under an arbitrary set of don't care words. We derive that from a more general result from which one also obtains an efficient minimization algorithm for deterministic parity automata with informative right-congruence (without don't care words). We then analyze languages of don't care words with a trivial right-congruence. For such sets of don't care words it is known that weak deterministic B\"uchi automata (WDBA) have a unique minimal automaton that can be efficiently computed from a given WDBA (Eisinger, Klaedtke 2006). We give a congruence-based characterization of the corresponding minimal WDBA, and show that the don't care minimization results for WDBA do not extend to deterministic $\omega$-automata with informative right-congruence: for this class there is no unique minimal automaton for a given don't care set with trivial right congruence, and the minimization problem is NP-hard. Finally, we extend an active learning algorithm for WDBA (Maler, Pnueli 1995) to the setting with an additional set of don't care words with trivial right-congruence.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Network Capacity Bound for Personalized PageRank in Multimodal Networks</title>
      <description><![CDATA[In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we deal with a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. We state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.]]></description>
      <pubDate>Sat, 01 Jul 2023 09:54:05 +0000</pubDate>
      <link>https://fi.episciences.org/11524</link>
      <guid>https://fi.episciences.org/11524</guid>
      <author>Kłopotek, M. A.</author>
      <author>Wierzchoń, S. T.</author>
      <author>Kłopotek, R. A.</author>
      <dc:creator>Kłopotek, M. A.</dc:creator>
      <dc:creator>Wierzchoń, S. T.</dc:creator>
      <dc:creator>Kłopotek, R. A.</dc:creator>
      <content:encoded><![CDATA[In a former paper the concept of Bipartite PageRank was introduced and a theorem on the limit of authority flowing between nodes for personalized PageRank has been generalized. In this paper we want to extend those results to multimodal networks. In particular we deal with a hypergraph type that may be used for describing multimodal network where a hyperlink connects nodes from each of the modalities. We introduce a generalisation of PageRank for such graphs and define the respective random walk model that can be used for computations. We state and prove theorems on the limit of outflow of authority for cases where individual modalities have identical and distinct damping factors.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Unfoldings and coverings of weighted graphs</title>
      <description><![CDATA[Coverings of undirected graphs are used in distributed computing, and unfoldings of directed graphs in semantics of programs. We study these two notions from a graph theoretical point of view so as to highlight their similarities, as they are both defined in terms of surjective graph homomorphisms. In particular, universal coverings and complete unfoldings are infinite trees that are regular if the initial graphs are finite. Regularity means that a tree has finitely many subtrees up to isomorphism. Two important theorems have been established by Leighton and Norris for coverings. We prove similar statements for unfoldings. Our study of the difficult proof of Leighton's Theorem lead us to generalize coverings and similarly, unfoldings, by attaching finite or infinite weights to edges of the covered or unfolded graphs. This generalization yields a canonical factorization of the universal covering of any finite graph, that (provably) does not exist without using weights. Introducing infinite weights provides us with finite descriptions of regular trees having nodes of countably infinite degree. We also generalize to weighted graphs and their coverings a classical factorization theorem of their characteristic polynomials.]]></description>
      <pubDate>Sat, 01 Jul 2023 09:52:49 +0000</pubDate>
      <link>https://fi.episciences.org/11360</link>
      <guid>https://fi.episciences.org/11360</guid>
      <author>Courcelle, Bruno</author>
      <dc:creator>Courcelle, Bruno</dc:creator>
      <content:encoded><![CDATA[Coverings of undirected graphs are used in distributed computing, and unfoldings of directed graphs in semantics of programs. We study these two notions from a graph theoretical point of view so as to highlight their similarities, as they are both defined in terms of surjective graph homomorphisms. In particular, universal coverings and complete unfoldings are infinite trees that are regular if the initial graphs are finite. Regularity means that a tree has finitely many subtrees up to isomorphism. Two important theorems have been established by Leighton and Norris for coverings. We prove similar statements for unfoldings. Our study of the difficult proof of Leighton's Theorem lead us to generalize coverings and similarly, unfoldings, by attaching finite or infinite weights to edges of the covered or unfolded graphs. This generalization yields a canonical factorization of the universal covering of any finite graph, that (provably) does not exist without using weights. Introducing infinite weights provides us with finite descriptions of regular trees having nodes of countably infinite degree. We also generalize to weighted graphs and their coverings a classical factorization theorem of their characteristic polynomials.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Maximal and minimal dynamic Petri net slicing</title>
      <description><![CDATA[Context: Petri net slicing is a technique to reduce the size of a Petri net to ease the analysis or understanding of the original Petri net. Objective: Presenting two new Petri net slicing algorithms to isolate those places and transitions of a Petri net (the slice) that may contribute tokens to one or more places given (the slicing criterion). Method: The two algorithms proposed are formalized. The maximality of the first algorithm and the minimality of the second algorithm are formally proven. Both algorithms, together with three other state-of-the-art algorithms, have been implemented and integrated into a single tool so that we have been able to carry out a fair empirical evaluation. Results: Besides the two new Petri net slicing algorithms, a public, free, and open-source implementation of five algorithms is reported. The results of an empirical evaluation of the new algorithms and the slices they produce are also presented. Conclusions: The first algorithm collects all places and transitions that may contribute tokens (in any computation) to the slicing criterion, while the second algorithm collects the places and transitions needed to fire the shortest transition sequence that contributes tokens to some place in the slicing criterion. Therefore, the net computed by the first algorithm can reproduce any computation that contributes tokens to any place of interest. In contrast, the second algorithm loses this possibility, but it often produces a much more reduced subnet (which still can reproduce some computations that contribute tokens to some places of interest). The first algorithm is proven maximal, and the second one is proven minimal.]]></description>
      <pubDate>Tue, 30 May 2023 14:24:22 +0000</pubDate>
      <link>https://fi.episciences.org/10934</link>
      <guid>https://fi.episciences.org/10934</guid>
      <author>Llorens, Marisa</author>
      <author>Oliver, Javier</author>
      <author>Silva, Josep</author>
      <author>Tamarit, Salvador</author>
      <dc:creator>Llorens, Marisa</dc:creator>
      <dc:creator>Oliver, Javier</dc:creator>
      <dc:creator>Silva, Josep</dc:creator>
      <dc:creator>Tamarit, Salvador</dc:creator>
      <content:encoded><![CDATA[Context: Petri net slicing is a technique to reduce the size of a Petri net to ease the analysis or understanding of the original Petri net. Objective: Presenting two new Petri net slicing algorithms to isolate those places and transitions of a Petri net (the slice) that may contribute tokens to one or more places given (the slicing criterion). Method: The two algorithms proposed are formalized. The maximality of the first algorithm and the minimality of the second algorithm are formally proven. Both algorithms, together with three other state-of-the-art algorithms, have been implemented and integrated into a single tool so that we have been able to carry out a fair empirical evaluation. Results: Besides the two new Petri net slicing algorithms, a public, free, and open-source implementation of five algorithms is reported. The results of an empirical evaluation of the new algorithms and the slices they produce are also presented. Conclusions: The first algorithm collects all places and transitions that may contribute tokens (in any computation) to the slicing criterion, while the second algorithm collects the places and transitions needed to fire the shortest transition sequence that contributes tokens to some place in the slicing criterion. Therefore, the net computed by the first algorithm can reproduce any computation that contributes tokens to any place of interest. In contrast, the second algorithm loses this possibility, but it often produces a much more reduced subnet (which still can reproduce some computations that contribute tokens to some places of interest). The first algorithm is proven maximal, and the second one is proven minimal.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Exact Wirelength of Embedding 3-Ary n-Cubes into certain Cylinders and Trees</title>
      <description><![CDATA[Graph embeddings play a significant role in the design and analysis of parallel algorithms. It is a mapping of the topological structure of a guest graph G into a host graph H, which is represented as a one-to-one mapping from the vertex set of the guest graph to the vertex set of the host graph. In multiprocessing systems the interconnection networks enhance the efficient communication between the components in the system. Obtaining minimum wirelength in embedding problems is significant in the designing of network and simulating one architecture by another. In this paper, we determine the wirelength of embedding 3-ary n-cubes into cylinders and certain trees.]]></description>
      <pubDate>Tue, 30 May 2023 14:23:40 +0000</pubDate>
      <link>https://fi.episciences.org/11289</link>
      <guid>https://fi.episciences.org/11289</guid>
      <author>S, Rajeshwari</author>
      <author>Rajesh, M</author>
      <dc:creator>S, Rajeshwari</dc:creator>
      <dc:creator>Rajesh, M</dc:creator>
      <content:encoded><![CDATA[Graph embeddings play a significant role in the design and analysis of parallel algorithms. It is a mapping of the topological structure of a guest graph G into a host graph H, which is represented as a one-to-one mapping from the vertex set of the guest graph to the vertex set of the host graph. In multiprocessing systems the interconnection networks enhance the efficient communication between the components in the system. Obtaining minimum wirelength in embedding problems is significant in the designing of network and simulating one architecture by another. In this paper, we determine the wirelength of embedding 3-ary n-cubes into cylinders and certain trees.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Formal Concepts and Residuation on Multilattices</title>
      <description><![CDATA[Multilattices are generalisations of lattices introduced by Mihail Benado. He replaced the existence of unique lower (resp. upper) bound by the existence of maximal lower (resp. minimal upper) bound(s). A multilattice will be called pure if it is not a lattice. Multilattices could be endowed with a residuation, and therefore used as set of truth-values to evaluate elements in fuzzy setting. In this paper we exhibit the smallest pure multilattice and show that it is a sub-multilattice of any pure multilattice. We also prove that any bounded residuated multilattice that is not a residuated lattice has at least seven elements. We apply the ordinal sum construction to get more examples of residuated multilattices that are not residuated lattices. We then use these residuated multilattices to evaluate objects and attributes in formal concept analysis setting, and describe the structure of the set of corresponding formal concepts. More precisely, if $\mathcal{A}_i: =(A_i,\le_i,\top_i,\odot_i,\to_i,\bot_i)$, $i=1,2$ are two complete residuated multilattices, $G$ and $M$ two nonempty sets and $(\varphi, \psi)$ a Galois connection between $A_1^G$ and $A_2^M$ that is compatible with the residuation, then we show that \[\mathcal{C}: =\{(h,f)\in A_1^G\times A_2^M; \varphi(h)=f \text{ and } \psi(f)=h \}\] can be endowed with a complete residuated multilattice structure. This is a generalization of a result by Ruiz-Calvi{\~n}o and Medina saying that if the (reduct of the) algebras $\mathcal{A}_i$, $i=1,2$ are complete multilattices, then $\mathcal{C}$ is a complete multilattice.]]></description>
      <pubDate>Tue, 30 May 2023 14:23:11 +0000</pubDate>
      <link>https://fi.episciences.org/11374</link>
      <guid>https://fi.episciences.org/11374</guid>
      <author>Njionou, Blaise B. Koguep</author>
      <author>Kwuida, Leonard</author>
      <author>Lele, Celestin</author>
      <dc:creator>Njionou, Blaise B. Koguep</dc:creator>
      <dc:creator>Kwuida, Leonard</dc:creator>
      <dc:creator>Lele, Celestin</dc:creator>
      <content:encoded><![CDATA[Multilattices are generalisations of lattices introduced by Mihail Benado. He replaced the existence of unique lower (resp. upper) bound by the existence of maximal lower (resp. minimal upper) bound(s). A multilattice will be called pure if it is not a lattice. Multilattices could be endowed with a residuation, and therefore used as set of truth-values to evaluate elements in fuzzy setting. In this paper we exhibit the smallest pure multilattice and show that it is a sub-multilattice of any pure multilattice. We also prove that any bounded residuated multilattice that is not a residuated lattice has at least seven elements. We apply the ordinal sum construction to get more examples of residuated multilattices that are not residuated lattices. We then use these residuated multilattices to evaluate objects and attributes in formal concept analysis setting, and describe the structure of the set of corresponding formal concepts. More precisely, if $\mathcal{A}_i: =(A_i,\le_i,\top_i,\odot_i,\to_i,\bot_i)$, $i=1,2$ are two complete residuated multilattices, $G$ and $M$ two nonempty sets and $(\varphi, \psi)$ a Galois connection between $A_1^G$ and $A_2^M$ that is compatible with the residuation, then we show that \[\mathcal{C}: =\{(h,f)\in A_1^G\times A_2^M; \varphi(h)=f \text{ and } \psi(f)=h \}\] can be endowed with a complete residuated multilattice structure. This is a generalization of a result by Ruiz-Calvi{\~n}o and Medina saying that if the (reduct of the) algebras $\mathcal{A}_i$, $i=1,2$ are complete multilattices, then $\mathcal{C}$ is a complete multilattice.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Structural Liveness of Immediate Observation Petri Nets</title>
      <description><![CDATA[We look in detail at the structural liveness problem (SLP) for subclasses of Petri nets, namely immediate observation nets (IO nets) and their generalized variant called branching immediate multi-observation nets (BIMO nets), that were recently introduced by Esparza, Raskin, and Weil-Kennedy. We show that SLP is PSPACE-hard for IO nets and in PSPACE for BIMO nets. In particular, we discuss the (small) bounds on the token numbers in net places that are decisive for a marking to be (non)live.]]></description>
      <pubDate>Tue, 18 Apr 2023 15:07:40 +0000</pubDate>
      <link>https://fi.episciences.org/11124</link>
      <guid>https://fi.episciences.org/11124</guid>
      <author>Jancar, Petr</author>
      <author>Valusek, Jiri</author>
      <dc:creator>Jancar, Petr</dc:creator>
      <dc:creator>Valusek, Jiri</dc:creator>
      <content:encoded><![CDATA[We look in detail at the structural liveness problem (SLP) for subclasses of Petri nets, namely immediate observation nets (IO nets) and their generalized variant called branching immediate multi-observation nets (BIMO nets), that were recently introduced by Esparza, Raskin, and Weil-Kennedy. We show that SLP is PSPACE-hard for IO nets and in PSPACE for BIMO nets. In particular, we discuss the (small) bounds on the token numbers in net places that are decisive for a marking to be (non)live.]]></content:encoded>
      <slash:comments>0</slash:comments>
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    <item>
      <title>Cost Automata, Safe Schemes, and Downward Closures</title>
      <description><![CDATA[In this work we prove decidability of the model-checking problem for safe recursion schemes against properties defined by alternating B-automata. We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes. Higher-order recursion schemes are an expressive formalism used to define languages of finite and infinite ranked trees by means of fixed points of lambda terms. They extend regular and context-free grammars, and are equivalent in expressive power to the simply typed $\lambda Y$-calculus and collapsible pushdown automata. Safety in a syntactic restriction which limits their expressive power. The class of alternating B-automata is an extension of alternating parity automata over infinite trees; it enhances them with counting features that can be used to describe boundedness properties.]]></description>
      <pubDate>Tue, 18 Apr 2023 15:07:17 +0000</pubDate>
      <link>https://fi.episciences.org/11157</link>
      <guid>https://fi.episciences.org/11157</guid>
      <author>Barozzini, David</author>
      <author>Clemente, Lorenzo</author>
      <author>Colcombet, Thomas</author>
      <author>Parys, Paweł</author>
      <dc:creator>Barozzini, David</dc:creator>
      <dc:creator>Clemente, Lorenzo</dc:creator>
      <dc:creator>Colcombet, Thomas</dc:creator>
      <dc:creator>Parys, Paweł</dc:creator>
      <content:encoded><![CDATA[In this work we prove decidability of the model-checking problem for safe recursion schemes against properties defined by alternating B-automata. We then exploit this result to show how to compute downward closures of languages of finite trees recognized by safe recursion schemes. Higher-order recursion schemes are an expressive formalism used to define languages of finite and infinite ranked trees by means of fixed points of lambda terms. They extend regular and context-free grammars, and are equivalent in expressive power to the simply typed $\lambda Y$-calculus and collapsible pushdown automata. Safety in a syntactic restriction which limits their expressive power. The class of alternating B-automata is an extension of alternating parity automata over infinite trees; it enhances them with counting features that can be used to describe boundedness properties.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Adaptive Merging on Phase Change Memory</title>
      <description><![CDATA[Indexing is a well-known database technique used to facilitate data access and speed up query processing. Nevertheless, the construction and modification of indexes are very expensive. In traditional approaches, all records in the database table are equally covered by the index. It is not effective, since some records may be queried very often and some never. To avoid this problem, adaptive merging has been introduced. The key idea is to create index adaptively and incrementally as a side-product of query processing. As a result, the database table is indexed partially depending on the query workload. This paper faces a problem of adaptive merging for phase change memory (PCM). The most important features of this memory type are: limited write endurance and high write latency. As a consequence, adaptive merging should be investigated from the scratch. We solve this problem in two steps. First, we apply several PCM optimization techniques to the traditional adaptive merging approach. We prove that the proposed method (eAM) outperforms a traditional approach by 60%. After that, we invent the framework for adaptive merging (PAM) and a new PCM-optimized index. It further improves the system performance by 20% for databases where search queries interleave with data modifications.]]></description>
      <pubDate>Tue, 07 Mar 2023 15:08:56 +0000</pubDate>
      <link>https://fi.episciences.org/11020</link>
      <guid>https://fi.episciences.org/11020</guid>
      <author>Macyna, Wojciech</author>
      <author>Kukowski, Michal</author>
      <dc:creator>Macyna, Wojciech</dc:creator>
      <dc:creator>Kukowski, Michal</dc:creator>
      <content:encoded><![CDATA[Indexing is a well-known database technique used to facilitate data access and speed up query processing. Nevertheless, the construction and modification of indexes are very expensive. In traditional approaches, all records in the database table are equally covered by the index. It is not effective, since some records may be queried very often and some never. To avoid this problem, adaptive merging has been introduced. The key idea is to create index adaptively and incrementally as a side-product of query processing. As a result, the database table is indexed partially depending on the query workload. This paper faces a problem of adaptive merging for phase change memory (PCM). The most important features of this memory type are: limited write endurance and high write latency. As a consequence, adaptive merging should be investigated from the scratch. We solve this problem in two steps. First, we apply several PCM optimization techniques to the traditional adaptive merging approach. We prove that the proposed method (eAM) outperforms a traditional approach by 60%. After that, we invent the framework for adaptive merging (PAM) and a new PCM-optimized index. It further improves the system performance by 20% for databases where search queries interleave with data modifications.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On Insecure Uses of BGN for Privacy Preserving Data Aggregation Protocols</title>
      <description><![CDATA[The notion of aggregator oblivious (AO) security for privacy preserving data aggregation was formalized with a specific construction of AO-secure blinding technique over a cyclic group by Shi et al. Some of proposals of data aggregation protocols use the blinding technique of Shi et al. for BGN cryptosystem, an additive homomorphic encryption. Previously, there have been some security analysis on some of BGN based data aggregation protocols in the context of integrity or authenticity of data. Even with such security analysis, the BGN cryptosystem has been a popular building block of privacy preserving data aggregation protocol. In this paper, we study the privacy issues in the blinding technique of Shi et al. used for BGN cryptosystem. We show that the blinding techniques for the BGN cryptosystem used in several protocols are not privacy preserving against the recipient, the decryptor. Our analysis is based on the fact that the BGN cryptosystem uses a pairing e:GxG-->G_T and the existence of the pairing makes the DDH problem on G easy to solve. We also suggest how to prevent such privacy leakage in the blinding technique of Shi et al. used for BGN cryptosystem.]]></description>
      <pubDate>Tue, 07 Mar 2023 15:08:35 +0000</pubDate>
      <link>https://fi.episciences.org/11027</link>
      <guid>https://fi.episciences.org/11027</guid>
      <author>Lee, Hyang-Sook</author>
      <author>Lim, Seongan</author>
      <author>Yie, Ikkwon</author>
      <author>Yun, Aaram</author>
      <dc:creator>Lee, Hyang-Sook</dc:creator>
      <dc:creator>Lim, Seongan</dc:creator>
      <dc:creator>Yie, Ikkwon</dc:creator>
      <dc:creator>Yun, Aaram</dc:creator>
      <content:encoded><![CDATA[The notion of aggregator oblivious (AO) security for privacy preserving data aggregation was formalized with a specific construction of AO-secure blinding technique over a cyclic group by Shi et al. Some of proposals of data aggregation protocols use the blinding technique of Shi et al. for BGN cryptosystem, an additive homomorphic encryption. Previously, there have been some security analysis on some of BGN based data aggregation protocols in the context of integrity or authenticity of data. Even with such security analysis, the BGN cryptosystem has been a popular building block of privacy preserving data aggregation protocol. In this paper, we study the privacy issues in the blinding technique of Shi et al. used for BGN cryptosystem. We show that the blinding techniques for the BGN cryptosystem used in several protocols are not privacy preserving against the recipient, the decryptor. Our analysis is based on the fact that the BGN cryptosystem uses a pairing e:GxG-->G_T and the existence of the pairing makes the DDH problem on G easy to solve. We also suggest how to prevent such privacy leakage in the blinding technique of Shi et al. used for BGN cryptosystem.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On Completeness of Cost Metrics and Meta-Search Algorithms in $-Calculus</title>
      <description><![CDATA[In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete (Diagonalization complete) and H-complete (Hypercomputation complete) classes. In the paper, in the spirit of Cook/Levin/Karp, we started the population process of these new classes assigning several undecidable problems to them. We justify that some super-Turing models of computation, i.e., models going beyond Turing machines, are tremendously expressive and they allow to accept arbitrary languages over a given alphabet including those undecidable ones. We prove also that one of such super-Turing models of computation - the \$-Calculus, designed as a tool for automatic problem solving and automatic programming, has also such tremendous expressiveness. We investigate also completeness of cost metrics and meta-search algorithms in \$-calculus.]]></description>
      <pubDate>Tue, 07 Mar 2023 15:08:07 +0000</pubDate>
      <link>https://fi.episciences.org/11033</link>
      <guid>https://fi.episciences.org/11033</guid>
      <author>Eberbach, Eugene</author>
      <dc:creator>Eberbach, Eugene</dc:creator>
      <content:encoded><![CDATA[In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete (Diagonalization complete) and H-complete (Hypercomputation complete) classes. In the paper, in the spirit of Cook/Levin/Karp, we started the population process of these new classes assigning several undecidable problems to them. We justify that some super-Turing models of computation, i.e., models going beyond Turing machines, are tremendously expressive and they allow to accept arbitrary languages over a given alphabet including those undecidable ones. We prove also that one of such super-Turing models of computation - the \$-Calculus, designed as a tool for automatic problem solving and automatic programming, has also such tremendous expressiveness. We investigate also completeness of cost metrics and meta-search algorithms in \$-calculus.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Towards Syntactic Epistemic Logic</title>
      <description><![CDATA[Traditionally, Epistemic Logic represents epistemic scenarios using a single model. This, however, covers only complete descriptions that specify truth values of all assertions. Indeed, many -- and perhaps most -- epistemic descriptions are not complete. Syntactic Epistemic Logic, SEL, suggests viewing an epistemic situation as a set of syntactic conditions rather than as a model. This allows us to naturally capture incomplete descriptions; we discuss a case study in which our proposal is successful. In Epistemic Game Theory, this closes the conceptual and technical gap, identified by R. Aumann, between the syntactic character of game-descriptions and semantic representations of games.]]></description>
      <pubDate>Tue, 10 Jan 2023 09:40:43 +0000</pubDate>
      <link>https://fi.episciences.org/10792</link>
      <guid>https://fi.episciences.org/10792</guid>
      <author>Artemov, Sergei</author>
      <dc:creator>Artemov, Sergei</dc:creator>
      <content:encoded><![CDATA[Traditionally, Epistemic Logic represents epistemic scenarios using a single model. This, however, covers only complete descriptions that specify truth values of all assertions. Indeed, many -- and perhaps most -- epistemic descriptions are not complete. Syntactic Epistemic Logic, SEL, suggests viewing an epistemic situation as a set of syntactic conditions rather than as a model. This allows us to naturally capture incomplete descriptions; we discuss a case study in which our proposal is successful. In Epistemic Game Theory, this closes the conceptual and technical gap, identified by R. Aumann, between the syntactic character of game-descriptions and semantic representations of games.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Universal Address Sequence Generator for Memory Built-in Self-test</title>
      <description><![CDATA[This paper presents the universal address sequence generator (UASG) for memory built-in-self-test. The studies are based on the proposed universal method for generating address sequences with the desired properties for multirun march memory tests. As a mathematical model, a modification of the recursive relation for quasi-random sequence generation is used. For this model, a structural diagram of the hardware implementation is given, of which the basis is a storage device for storing so-called direction numbers of the generation matrix. The form of the generation matrix determines the basic properties of the generated address sequences. The proposed UASG generates a wide spectrum of different address sequences, including the standard ones, such as linear, address complement, gray code, worst-case gate delay, $2^i$, next address, and pseudorandom. Examples of the use of the proposed methods are considered. The result of the practical implementation of the UASG is presented, and the main characteristics are evaluated.]]></description>
      <pubDate>Tue, 10 Jan 2023 09:29:54 +0000</pubDate>
      <link>https://fi.episciences.org/10773</link>
      <guid>https://fi.episciences.org/10773</guid>
      <author>Mrozek, I.</author>
      <author>Shevchenko, N. A.</author>
      <author>Yarmolik, V. N.</author>
      <dc:creator>Mrozek, I.</dc:creator>
      <dc:creator>Shevchenko, N. A.</dc:creator>
      <dc:creator>Yarmolik, V. N.</dc:creator>
      <content:encoded><![CDATA[This paper presents the universal address sequence generator (UASG) for memory built-in-self-test. The studies are based on the proposed universal method for generating address sequences with the desired properties for multirun march memory tests. As a mathematical model, a modification of the recursive relation for quasi-random sequence generation is used. For this model, a structural diagram of the hardware implementation is given, of which the basis is a storage device for storing so-called direction numbers of the generation matrix. The form of the generation matrix determines the basic properties of the generated address sequences. The proposed UASG generates a wide spectrum of different address sequences, including the standard ones, such as linear, address complement, gray code, worst-case gate delay, $2^i$, next address, and pseudorandom. Examples of the use of the proposed methods are considered. The result of the practical implementation of the UASG is presented, and the main characteristics are evaluated.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A note on calculi for non-deterministic many-valued logics</title>
      <description><![CDATA[We present two deductively equivalent calculi for non-deterministic many-valued logics. One is defined by axioms and the other - by rules of inference. The two calculi are obtained from the truth tables of the logic under consideration in a straightforward manner. We prove soundness and strong completeness theorems for both calculi and also prove the cut elimination theorem for the calculi defined by rules of inference.]]></description>
      <pubDate>Mon, 02 Jan 2023 16:52:36 +0000</pubDate>
      <link>https://fi.episciences.org/10760</link>
      <guid>https://fi.episciences.org/10760</guid>
      <author>Kaminski, Michael</author>
      <dc:creator>Kaminski, Michael</dc:creator>
      <content:encoded><![CDATA[We present two deductively equivalent calculi for non-deterministic many-valued logics. One is defined by axioms and the other - by rules of inference. The two calculi are obtained from the truth tables of the logic under consideration in a straightforward manner. We prove soundness and strong completeness theorems for both calculi and also prove the cut elimination theorem for the calculi defined by rules of inference.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Decidability of definability issues in the theory of real addition</title>
      <description><![CDATA[Given a subset of $X\subseteq \mathbb{R}^{n}$ we can associate with every point $x\in \mathbb{R}^{n}$ a vector space $V$ of maximal dimension with the property that for some ball centered at $x$, the subset $X$ coincides inside the ball with a union of lines parallel with $V$. A point is singular if $V$ has dimension $0$. In an earlier paper we proved that a $(\mathbb{R}, +,< ,\mathbb{Z})$-definable relation $X$ is actually definable in $(\mathbb{R}, +,< ,1)$ if and only if the number of singular points is finite and every rational section of $X$ is $(\mathbb{R}, +,< ,1)$-definable, where a rational section is a set obtained from $X$ by fixing some component to a rational value. Here we show that we can dispense with the hypothesis of $X$ being $(\mathbb{R}, +,< ,\mathbb{Z})$-definable by assuming that the components of the singular points are rational numbers. This provides a topological characterization of first-order definability in the structure $(\mathbb{R}, +,< ,1)$. It also allows us to deliver a self-definable criterion (in Muchnik's terminology) of $(\mathbb{R}, +,< ,1)$- and $(\mathbb{R}, +,< ,\mathbb{Z})$-definability for a wide class of relations, which turns into an effective criterion provided that the corresponding theory is decidable. In particular these results apply to the class of $k-$recognizable relations on reals, and allow us to prove that it is decidable whether a $k-$recognizable relation (of any arity) is $l-$recognizable for every base $l \geq 2$.]]></description>
      <pubDate>Fri, 30 Dec 2022 08:39:40 +0000</pubDate>
      <link>https://fi.episciences.org/10753</link>
      <guid>https://fi.episciences.org/10753</guid>
      <author>Bès, Alexis</author>
      <author>Choffrut, Christian</author>
      <dc:creator>Bès, Alexis</dc:creator>
      <dc:creator>Choffrut, Christian</dc:creator>
      <content:encoded><![CDATA[Given a subset of $X\subseteq \mathbb{R}^{n}$ we can associate with every point $x\in \mathbb{R}^{n}$ a vector space $V$ of maximal dimension with the property that for some ball centered at $x$, the subset $X$ coincides inside the ball with a union of lines parallel with $V$. A point is singular if $V$ has dimension $0$. In an earlier paper we proved that a $(\mathbb{R}, +,< ,\mathbb{Z})$-definable relation $X$ is actually definable in $(\mathbb{R}, +,< ,1)$ if and only if the number of singular points is finite and every rational section of $X$ is $(\mathbb{R}, +,< ,1)$-definable, where a rational section is a set obtained from $X$ by fixing some component to a rational value. Here we show that we can dispense with the hypothesis of $X$ being $(\mathbb{R}, +,< ,\mathbb{Z})$-definable by assuming that the components of the singular points are rational numbers. This provides a topological characterization of first-order definability in the structure $(\mathbb{R}, +,< ,1)$. It also allows us to deliver a self-definable criterion (in Muchnik's terminology) of $(\mathbb{R}, +,< ,1)$- and $(\mathbb{R}, +,< ,\mathbb{Z})$-definability for a wide class of relations, which turns into an effective criterion provided that the corresponding theory is decidable. In particular these results apply to the class of $k-$recognizable relations on reals, and allow us to prove that it is decidable whether a $k-$recognizable relation (of any arity) is $l-$recognizable for every base $l \geq 2$.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On finding hamiltonian cycles in Barnette graphs</title>
      <description><![CDATA[In this paper, we deal with hamiltonicity in planar cubic graphs G having a facial 2-factor Q via (quasi) spanning trees of faces in G/Q and study the algorithmic complexity of finding such (quasi) spanning trees of faces. Moreover, we show that if Barnette's Conjecture is false, then hamiltonicity in 3-connected planar cubic bipartite graphs is an NP-complete problem.]]></description>
      <pubDate>Thu, 15 Dec 2022 09:23:34 +0000</pubDate>
      <link>https://fi.episciences.org/10485</link>
      <guid>https://fi.episciences.org/10485</guid>
      <author>Gh., Behrooz Bagheri</author>
      <author>Feder, Tomas</author>
      <author>Fleischner, Herbert</author>
      <author>Subi, Carlos</author>
      <dc:creator>Gh., Behrooz Bagheri</dc:creator>
      <dc:creator>Feder, Tomas</dc:creator>
      <dc:creator>Fleischner, Herbert</dc:creator>
      <dc:creator>Subi, Carlos</dc:creator>
      <content:encoded><![CDATA[In this paper, we deal with hamiltonicity in planar cubic graphs G having a facial 2-factor Q via (quasi) spanning trees of faces in G/Q and study the algorithmic complexity of finding such (quasi) spanning trees of faces. Moreover, we show that if Barnette's Conjecture is false, then hamiltonicity in 3-connected planar cubic bipartite graphs is an NP-complete problem.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Computing Parameterized Invariants of Parameterized Petri Nets</title>
      <description><![CDATA[A fundamental advantage of Petri net models is the possibility to automatically compute useful system invariants from the syntax of the net. Classical techniques used for this are place invariants, P-components, siphons or traps. Recently, Bozga et al. have presented a novel technique for the \emph{parameterized} verification of safety properties of systems with a ring or array architecture. They show that the statement \enquote{for every instance of the parameterized Petri net, all markings satisfying the linear invariants associated to all the P-components, siphons and traps of the instance are safe} can be encoded in \acs{WS1S} and checked using tools like MONA. However, while the technique certifies that this infinite set of linear invariants extracted from P-components, siphons or traps are strong enough to prove safety, it does not return an explanation of this fact understandable by humans. We present a CEGAR loop that constructs a \emph{finite} set of \emph{parameterized} P-components, siphons or traps, whose infinitely many instances are strong enough to prove safety. For this we design parameterization procedures for different architectures.]]></description>
      <pubDate>Thu, 27 Oct 2022 07:05:38 +0000</pubDate>
      <link>https://fi.episciences.org/10196</link>
      <guid>https://fi.episciences.org/10196</guid>
      <author>Esparza, Javier</author>
      <author>Raskin, Mikhail</author>
      <author>Welzel, Christoph</author>
      <dc:creator>Esparza, Javier</dc:creator>
      <dc:creator>Raskin, Mikhail</dc:creator>
      <dc:creator>Welzel, Christoph</dc:creator>
      <content:encoded><![CDATA[A fundamental advantage of Petri net models is the possibility to automatically compute useful system invariants from the syntax of the net. Classical techniques used for this are place invariants, P-components, siphons or traps. Recently, Bozga et al. have presented a novel technique for the \emph{parameterized} verification of safety properties of systems with a ring or array architecture. They show that the statement \enquote{for every instance of the parameterized Petri net, all markings satisfying the linear invariants associated to all the P-components, siphons and traps of the instance are safe} can be encoded in \acs{WS1S} and checked using tools like MONA. However, while the technique certifies that this infinite set of linear invariants extracted from P-components, siphons or traps are strong enough to prove safety, it does not return an explanation of this fact understandable by humans. We present a CEGAR loop that constructs a \emph{finite} set of \emph{parameterized} P-components, siphons or traps, whose infinitely many instances are strong enough to prove safety. For this we design parameterization procedures for different architectures.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Skeleton Abstraction for Universal Temporal Properties</title>
      <description><![CDATA[Uniform coloured Petri nets can be abstracted to their skeleton, the place/transition net that simply turns the coloured tokens into black tokens. A coloured net and its skeleton are related by a net morphism. For the application of the skeleton as an abstraction method in the model checking process, we need to establish a simulation relation between the state spaces of the two nets. Then, universal temporal properties (properties of the $ ACTL^* $ logic) are preserved. The abstraction relation induced by a net morphism is not necessarily a simulation relation, due to a subtle issue related to deadlocks. We discuss several situations where the abstraction relation induced by a net morphism is as well a simulation relation, thus preserving $ACTL^*$ properties. We further propose a partition refinement algorithm for folding a place/transition net into a coloured net. This way, skeleton abstraction becomes available for models given as place/transition nets. Experiments demonstrate the capabilities of the proposed technology. Using skeleton abstraction, we are capable of solving problems that have not been solved before in the Model Checking Contest.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:08:34 +0000</pubDate>
      <link>https://fi.episciences.org/10157</link>
      <guid>https://fi.episciences.org/10157</guid>
      <author>Wallner, Sophie</author>
      <author>Wolf, Karsten</author>
      <dc:creator>Wallner, Sophie</dc:creator>
      <dc:creator>Wolf, Karsten</dc:creator>
      <content:encoded><![CDATA[Uniform coloured Petri nets can be abstracted to their skeleton, the place/transition net that simply turns the coloured tokens into black tokens. A coloured net and its skeleton are related by a net morphism. For the application of the skeleton as an abstraction method in the model checking process, we need to establish a simulation relation between the state spaces of the two nets. Then, universal temporal properties (properties of the $ ACTL^* $ logic) are preserved. The abstraction relation induced by a net morphism is not necessarily a simulation relation, due to a subtle issue related to deadlocks. We discuss several situations where the abstraction relation induced by a net morphism is as well a simulation relation, thus preserving $ACTL^*$ properties. We further propose a partition refinement algorithm for folding a place/transition net into a coloured net. This way, skeleton abstraction becomes available for models given as place/transition nets. Experiments demonstrate the capabilities of the proposed technology. Using skeleton abstraction, we are capable of solving problems that have not been solved before in the Model Checking Contest.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Some Basic Techniques allowing Petri Net Synthesis: Complexity and Algorithmic Issues</title>
      <description><![CDATA[In Petri net synthesis we ask whether a given transition system $A$ can be implemented by a Petri net $N$. Depending on the level of accuracy, there are three ways how $N$ can implement $A$: an embedding, the least accurate implementation, preserves only the diversity of states of $A$; a language simulation already preserves exactly the language of $A$; a realization, the most accurate implementation, realizes the behavior of $A$ exactly. However, whatever the sought implementation, a corresponding net does not always exist. In this case, it was suggested to modify the input behavior -- of course as little as possible. Since transition systems consist of states, events and edges, these components appear as a natural choice for modifications. In this paper we show that the task of converting an unimplementable transition system into an implementable one by removing as few states or events or edges as possible is NP-complete -- regardless of what type of implementation we are aiming for; we also show that the corresponding parameterized problems are $W[2]$-hard, where the number of removed components is considered as the parameter; finally, we show there is no $c$-approximation algorithm (with a polynomial running time) for neither of these problems, for every constant $c\geq 1$.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:08:15 +0000</pubDate>
      <link>https://fi.episciences.org/10138</link>
      <guid>https://fi.episciences.org/10138</guid>
      <author>Devillers, Raymond</author>
      <author>Tredup, Ronny</author>
      <dc:creator>Devillers, Raymond</dc:creator>
      <dc:creator>Tredup, Ronny</dc:creator>
      <content:encoded><![CDATA[In Petri net synthesis we ask whether a given transition system $A$ can be implemented by a Petri net $N$. Depending on the level of accuracy, there are three ways how $N$ can implement $A$: an embedding, the least accurate implementation, preserves only the diversity of states of $A$; a language simulation already preserves exactly the language of $A$; a realization, the most accurate implementation, realizes the behavior of $A$ exactly. However, whatever the sought implementation, a corresponding net does not always exist. In this case, it was suggested to modify the input behavior -- of course as little as possible. Since transition systems consist of states, events and edges, these components appear as a natural choice for modifications. In this paper we show that the task of converting an unimplementable transition system into an implementable one by removing as few states or events or edges as possible is NP-complete -- regardless of what type of implementation we are aiming for; we also show that the corresponding parameterized problems are $W[2]$-hard, where the number of removed components is considered as the parameter; finally, we show there is no $c$-approximation algorithm (with a polynomial running time) for neither of these problems, for every constant $c\geq 1$.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Synthesis of Pure and Impure Petri nets With Restricted Place-environments: Complexity Issues</title>
      <description><![CDATA[Petri net synthesis consists in deciding for a given transition system $A$ whether there exists a Petri net $N$ whose reachability graph is isomorphic to $A$. Several works examined the synthesis of Petri net subclasses that restrict, for every place $p$ of the net, the cardinality of its preset or of its postset or both in advance by small natural numbers $\varrho$ and $\kappa$, respectively, such as for example (weighted) marked graphs, (weighted) T-systems and choice-free nets. In this paper, we study the synthesis aiming at Petri nets which have such restricted place environments, from the viewpoint of classical and parameterized complexity: We first show that, for any fixed natural numbers $\varrho$ and $\kappa$, deciding whether for a given transition system $A$ there is a Petri net $N$ such that (1) its reachability graph is isomorphic to $A$ and (2) for every place $p$ of $N$ the preset of $p$ has at most $\varrho$ and the postset of $p$ has at most $\kappa$ elements is doable in polynomial time. Secondly, we introduce a modified version of the problem, namely Environment Restricted Synthesis (ERS, for short), where $\varrho$ and $\kappa$ are part of the input, and show that ERS is NP-complete, regardless whether the sought net is impure or pure. In case of the impure nets, our methods also imply that ERS parameterized by $\varrho+\kappa$ is $W[2]$-hard.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:07:54 +0000</pubDate>
      <link>https://fi.episciences.org/10139</link>
      <guid>https://fi.episciences.org/10139</guid>
      <author>Devillers, Raymond</author>
      <author>Tredup, Ronny</author>
      <dc:creator>Devillers, Raymond</dc:creator>
      <dc:creator>Tredup, Ronny</dc:creator>
      <content:encoded><![CDATA[Petri net synthesis consists in deciding for a given transition system $A$ whether there exists a Petri net $N$ whose reachability graph is isomorphic to $A$. Several works examined the synthesis of Petri net subclasses that restrict, for every place $p$ of the net, the cardinality of its preset or of its postset or both in advance by small natural numbers $\varrho$ and $\kappa$, respectively, such as for example (weighted) marked graphs, (weighted) T-systems and choice-free nets. In this paper, we study the synthesis aiming at Petri nets which have such restricted place environments, from the viewpoint of classical and parameterized complexity: We first show that, for any fixed natural numbers $\varrho$ and $\kappa$, deciding whether for a given transition system $A$ there is a Petri net $N$ such that (1) its reachability graph is isomorphic to $A$ and (2) for every place $p$ of $N$ the preset of $p$ has at most $\varrho$ and the postset of $p$ has at most $\kappa$ elements is doable in polynomial time. Secondly, we introduce a modified version of the problem, namely Environment Restricted Synthesis (ERS, for short), where $\varrho$ and $\kappa$ are part of the input, and show that ERS is NP-complete, regardless whether the sought net is impure or pure. In case of the impure nets, our methods also imply that ERS parameterized by $\varrho+\kappa$ is $W[2]$-hard.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A Polyhedral Abstraction for Petri nets and its Application to SMT-Based Model Checking</title>
      <description><![CDATA[We define a new method for taking advantage of net reductions in combination with a SMT-based model checker. Our approach consists in transforming a reachability problem about some Petri net, into the verification of an updated reachability property on a reduced version of this net. This method relies on a new state space abstraction based on systems of constraints, called polyhedral abstraction. We prove the correctness of this method using a new notion of equivalence between nets. We provide a complete framework to define and check the correctness of equivalence judgements; prove that this relation is a congruence; and give examples of basic equivalence relations that derive from structural reductions. Our approach has been implemented in a tool, named SMPT, that provides two main procedures: Bounded Model Checking (BMC) and Property Directed Reachability (PDR). Each procedure has been adapted in order to use reductions and to work with arbitrary Petri nets. We tested SMPT on a large collection of queries used in the Model Checking Contest. Our experimental results show that our approach works well, even when we only have a moderate amount of reductions.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:07:37 +0000</pubDate>
      <link>https://fi.episciences.org/10141</link>
      <guid>https://fi.episciences.org/10141</guid>
      <author>Amat, Nicolas</author>
      <author>Berthomieu, Bernard</author>
      <author>Zilio, Silvano Dal</author>
      <dc:creator>Amat, Nicolas</dc:creator>
      <dc:creator>Berthomieu, Bernard</dc:creator>
      <dc:creator>Zilio, Silvano Dal</dc:creator>
      <content:encoded><![CDATA[We define a new method for taking advantage of net reductions in combination with a SMT-based model checker. Our approach consists in transforming a reachability problem about some Petri net, into the verification of an updated reachability property on a reduced version of this net. This method relies on a new state space abstraction based on systems of constraints, called polyhedral abstraction. We prove the correctness of this method using a new notion of equivalence between nets. We provide a complete framework to define and check the correctness of equivalence judgements; prove that this relation is a congruence; and give examples of basic equivalence relations that derive from structural reductions. Our approach has been implemented in a tool, named SMPT, that provides two main procedures: Bounded Model Checking (BMC) and Property Directed Reachability (PDR). Each procedure has been adapted in order to use reductions and to work with arbitrary Petri nets. We tested SMPT on a large collection of queries used in the Model Checking Contest. Our experimental results show that our approach works well, even when we only have a moderate amount of reductions.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Introduction to probabilistic concurrent systems</title>
      <description><![CDATA[The first part of the paper is an introduction to the theory of probabilistic concurrent systems under a partial order semantics. Key definitions and results are given and illustrated on examples. The second part includes contributions. We introduce deterministic concurrent systems as a subclass of concurrent systems. Deterministic concurrent system are "locally commutative'" concurrent systems. We prove that irreducible and deterministic concurrent systems have a unique probabilistic dynamics, and we characterize these systems by means of their combinatorial properties.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:06:14 +0000</pubDate>
      <link>https://fi.episciences.org/10136</link>
      <guid>https://fi.episciences.org/10136</guid>
      <author>Abbes, Samy</author>
      <dc:creator>Abbes, Samy</dc:creator>
      <content:encoded><![CDATA[The first part of the paper is an introduction to the theory of probabilistic concurrent systems under a partial order semantics. Key definitions and results are given and illustrated on examples. The second part includes contributions. We introduce deterministic concurrent systems as a subclass of concurrent systems. Deterministic concurrent system are "locally commutative'" concurrent systems. We prove that irreducible and deterministic concurrent systems have a unique probabilistic dynamics, and we characterize these systems by means of their combinatorial properties.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A note of generalization of fractional ID-factor-critical graphs</title>
      <description><![CDATA[In communication networks, the binding numbers of graphs (or networks) are often used to measure the vulnerability and robustness of graphs (or networks). Furthermore, the fractional factors of graphs and the fractional ID-$[a,b]$-factor-critical covered graphs have a great deal of important applications in the data transmission networks. In this paper, we investigate the relationship between the binding numbers of graphs and the fractional ID-$[a,b]$-factor-critical covered graphs, and derive a binding number condition for a graph to be fractional ID-$[a,b]$-factor-critical covered, which is an extension of Zhou's previous result [S. Zhou, Binding numbers for fractional ID-$k$-factor-critical graphs, Acta Mathematica Sinica, English Series 30(1)(2014)181--186].]]></description>
      <pubDate>Fri, 21 Oct 2022 20:05:42 +0000</pubDate>
      <link>https://fi.episciences.org/9991</link>
      <guid>https://fi.episciences.org/9991</guid>
      <author>Zhou, Sizhong</author>
      <dc:creator>Zhou, Sizhong</dc:creator>
      <content:encoded><![CDATA[In communication networks, the binding numbers of graphs (or networks) are often used to measure the vulnerability and robustness of graphs (or networks). Furthermore, the fractional factors of graphs and the fractional ID-$[a,b]$-factor-critical covered graphs have a great deal of important applications in the data transmission networks. In this paper, we investigate the relationship between the binding numbers of graphs and the fractional ID-$[a,b]$-factor-critical covered graphs, and derive a binding number condition for a graph to be fractional ID-$[a,b]$-factor-critical covered, which is an extension of Zhou's previous result [S. Zhou, Binding numbers for fractional ID-$k$-factor-critical graphs, Acta Mathematica Sinica, English Series 30(1)(2014)181--186].]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Number Conservation via Particle Flow in One-dimensional Cellular Automata</title>
      <description><![CDATA[A number-conserving cellular automaton is a simplified model for a system of interacting particles. This paper contains two related constructions by which one can find all one-dimensional number-conserving cellular automata with one kind of particle. The output of both methods is a "flow function", which describes the movement of the particles. In the first method, one puts increasingly stronger restrictions on the particle flow until a single flow function is specified. There are no dead ends, every choice of restriction steps ends with a flow. The second method uses the fact that the flow functions can be ordered and then form a lattice. This method consists of a recipe for the slowest flow that enforces a given minimal particle speed in one given neighbourhood. All other flow functions are then maxima of sets of these flows. Other questions, like that about the nature of non-deterministic number-conserving rules, are treated briefly at the end.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:05:20 +0000</pubDate>
      <link>https://fi.episciences.org/9992</link>
      <guid>https://fi.episciences.org/9992</guid>
      <author>Redeker, Markus</author>
      <dc:creator>Redeker, Markus</dc:creator>
      <content:encoded><![CDATA[A number-conserving cellular automaton is a simplified model for a system of interacting particles. This paper contains two related constructions by which one can find all one-dimensional number-conserving cellular automata with one kind of particle. The output of both methods is a "flow function", which describes the movement of the particles. In the first method, one puts increasingly stronger restrictions on the particle flow until a single flow function is specified. There are no dead ends, every choice of restriction steps ends with a flow. The second method uses the fact that the flow functions can be ordered and then form a lattice. This method consists of a recipe for the slowest flow that enforces a given minimal particle speed in one given neighbourhood. All other flow functions are then maxima of sets of these flows. Other questions, like that about the nature of non-deterministic number-conserving rules, are treated briefly at the end.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Gathering over Meeting Nodes in Infinite Grid</title>
      <description><![CDATA[The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:05:00 +0000</pubDate>
      <link>https://fi.episciences.org/10001</link>
      <guid>https://fi.episciences.org/10001</guid>
      <author>Bhagat, Subhash</author>
      <author>Chakraborty, Abhinav</author>
      <author>Das, Bibhuti</author>
      <author>Mukhopadhyaya, Krishnendu</author>
      <dc:creator>Bhagat, Subhash</dc:creator>
      <dc:creator>Chakraborty, Abhinav</dc:creator>
      <dc:creator>Das, Bibhuti</dc:creator>
      <dc:creator>Mukhopadhyaya, Krishnendu</dc:creator>
      <content:encoded><![CDATA[The gathering over meeting nodes problem asks the robots to gather at one of the pre-defined meeting nodes. The robots are deployed on the nodes of an anonymous two-dimensional infinite grid which has a subset of nodes marked as meeting nodes. Robots are identical, autonomous, anonymous and oblivious. They operate under an asynchronous scheduler. They do not have any agreement on a global coordinate system. All the initial configurations for which the problem is deterministically unsolvable have been characterized. A deterministic distributed algorithm has been proposed to solve the problem for the remaining configurations. The efficiency of the proposed algorithm is studied in terms of the number of moves required for gathering. A lower bound concerning the total number of moves required to solve the gathering problem has been derived.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Boris (Boaz) Trakhtenbrot -- The Beginning</title>
      <description><![CDATA[This memorial paper tells the story of the beginning of Boris (Boaz) Trakhtenbrot's long and rich life path, full of unusual and sometimes tragic events. This path led a boy from a Jewish settlement in Eastern Europe to be recognized as one of the founding fathers of theoretical computer science.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:04:20 +0000</pubDate>
      <link>https://fi.episciences.org/10083</link>
      <guid>https://fi.episciences.org/10083</guid>
      <author>Trakhtenbrot, Mark</author>
      <dc:creator>Trakhtenbrot, Mark</dc:creator>
      <content:encoded><![CDATA[This memorial paper tells the story of the beginning of Boris (Boaz) Trakhtenbrot's long and rich life path, full of unusual and sometimes tragic events. This path led a boy from a Jewish settlement in Eastern Europe to be recognized as one of the founding fathers of theoretical computer science.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Morphisms and minimisation of weighted automata</title>
      <description><![CDATA[This paper studies the algorithms for the minimisation of weighted automata. It starts with the definition of morphisms-which generalises and unifies the notion of bisimulation to the whole class of weighted automata-and the unicity of a minimal quotient for every automaton, obtained by partition refinement. From a general scheme for the refinement of partitions, two strategies are considered for the computation of the minimal quotient: the Domain Split and the Predecesor Class Split algorithms. They correspond respectivly to the classical Moore and Hopcroft algorithms for the computation of the minimal quotient of deterministic Boolean automata. We show that these two strategies yield algorithms with the same quadratic complexity and we study the cases when the second one can be improved in order to achieve a complexity similar to the one of Hopcroft algorithm.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:04:02 +0000</pubDate>
      <link>https://fi.episciences.org/9972</link>
      <guid>https://fi.episciences.org/9972</guid>
      <author>Lombardy, Sylvain</author>
      <author>Sakarovitch, Jacques</author>
      <dc:creator>Lombardy, Sylvain</dc:creator>
      <dc:creator>Sakarovitch, Jacques</dc:creator>
      <content:encoded><![CDATA[This paper studies the algorithms for the minimisation of weighted automata. It starts with the definition of morphisms-which generalises and unifies the notion of bisimulation to the whole class of weighted automata-and the unicity of a minimal quotient for every automaton, obtained by partition refinement. From a general scheme for the refinement of partitions, two strategies are considered for the computation of the minimal quotient: the Domain Split and the Predecesor Class Split algorithms. They correspond respectivly to the classical Moore and Hopcroft algorithms for the computation of the minimal quotient of deterministic Boolean automata. We show that these two strategies yield algorithms with the same quadratic complexity and we study the cases when the second one can be improved in order to achieve a complexity similar to the one of Hopcroft algorithm.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Resource Bisimilarity in Petri Nets is Decidable</title>
      <description><![CDATA[Petri nets are a popular formalism for modeling and analyzing distributed systems. Tokens in Petri net models can represent the control flow state or resources produced/consumed by transition firings. We define a resource as a part (a submultiset) of Petri net markings and call two resources equivalent when replacing one of them with another in any marking does not change the observable Petri net behavior. We consider resource similarity and resource bisimilarity, two congruent restrictions of bisimulation equivalence on Petri net markings. Previously it was proved that resource similarity (the largest congruence included in bisimulation equivalence) is undecidable. Here we present an algorithm for checking resource bisimilarity, thereby proving that this relation (the largest congruence included in bisimulation equivalence that is a bisimulation) is decidable. We also give an example of two resources in a Petri net that are similar but not bisimilar.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:03:40 +0000</pubDate>
      <link>https://fi.episciences.org/9954</link>
      <guid>https://fi.episciences.org/9954</guid>
      <author>Lomazova, Irina</author>
      <author>Bashkin, Vladimir</author>
      <author>Jančar, Petr</author>
      <dc:creator>Lomazova, Irina</dc:creator>
      <dc:creator>Bashkin, Vladimir</dc:creator>
      <dc:creator>Jančar, Petr</dc:creator>
      <content:encoded><![CDATA[Petri nets are a popular formalism for modeling and analyzing distributed systems. Tokens in Petri net models can represent the control flow state or resources produced/consumed by transition firings. We define a resource as a part (a submultiset) of Petri net markings and call two resources equivalent when replacing one of them with another in any marking does not change the observable Petri net behavior. We consider resource similarity and resource bisimilarity, two congruent restrictions of bisimulation equivalence on Petri net markings. Previously it was proved that resource similarity (the largest congruence included in bisimulation equivalence) is undecidable. Here we present an algorithm for checking resource bisimilarity, thereby proving that this relation (the largest congruence included in bisimulation equivalence that is a bisimulation) is decidable. We also give an example of two resources in a Petri net that are similar but not bisimilar.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On the Tutte and matching polynomials for complete graphs</title>
      <description><![CDATA[Let $T(G;X,Y)$ be the Tutte polynomial for graphs. We study the sequence $t_{a,b}(n) = T(K_n;a,b)$ where $a,b$ are non-negative integers, and show that for every $\mu \in \N$ the sequence $t_{a,b}(n)$ is ultimately periodic modulo $\mu$ provided $a \neq 1 \mod{\mu}$ and $b \neq 1 \mod{\mu}$. This result is related to a conjecture by A. Mani and R. Stones from 2016. The theorem is a consequence of a more general theorem which holds for a wide class of graph polynomials definable in Monadic Second Order Logic and some of its extensions, such as the the independence polynomial, the clique polynomial, etc. We also show similar results for the various substitution instances of the bivariate matching polynomial and the trivariate edge elimination polynomial $\xi(G;X,Y,Z)$ introduced by I. Averbouch, B. Godlin and the second author in 2008. All our results depend on the Specker-Blatter Theorem from 1981, which studies modular recurrence relations of combinatorial sequences which count the number of labeled graphs.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:02:58 +0000</pubDate>
      <link>https://fi.episciences.org/8839</link>
      <guid>https://fi.episciences.org/8839</guid>
      <author>Kotek, Tomer</author>
      <author>Makowsky, Johann A.</author>
      <dc:creator>Kotek, Tomer</dc:creator>
      <dc:creator>Makowsky, Johann A.</dc:creator>
      <content:encoded><![CDATA[Let $T(G;X,Y)$ be the Tutte polynomial for graphs. We study the sequence $t_{a,b}(n) = T(K_n;a,b)$ where $a,b$ are non-negative integers, and show that for every $\mu \in \N$ the sequence $t_{a,b}(n)$ is ultimately periodic modulo $\mu$ provided $a \neq 1 \mod{\mu}$ and $b \neq 1 \mod{\mu}$. This result is related to a conjecture by A. Mani and R. Stones from 2016. The theorem is a consequence of a more general theorem which holds for a wide class of graph polynomials definable in Monadic Second Order Logic and some of its extensions, such as the the independence polynomial, the clique polynomial, etc. We also show similar results for the various substitution instances of the bivariate matching polynomial and the trivariate edge elimination polynomial $\xi(G;X,Y,Z)$ introduced by I. Averbouch, B. Godlin and the second author in 2008. All our results depend on the Specker-Blatter Theorem from 1981, which studies modular recurrence relations of combinatorial sequences which count the number of labeled graphs.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>The 1966 International Congress of Mathematicians: A micro-memoir</title>
      <description><![CDATA[To an extent, the 1966 congress was a hole in the iron curtain. At least that how a young Soviet mathematician saw it.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:02:37 +0000</pubDate>
      <link>https://fi.episciences.org/9961</link>
      <guid>https://fi.episciences.org/9961</guid>
      <author>Gurevich, Yuri</author>
      <dc:creator>Gurevich, Yuri</dc:creator>
      <content:encoded><![CDATA[To an extent, the 1966 congress was a hole in the iron curtain. At least that how a young Soviet mathematician saw it.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Order-theoretic trees: monadic second-order descriptions and regularity</title>
      <description><![CDATA[An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any countable linear order. Such generalized infinite trees yield convenient definitions of the rank-width and the modular decomposition of countable graphs. We define an algebra based on only four operations that generate up to isomorphism and via infinite terms these order-theoretic trees and forests. We prove that the associated regular objects, those defined by regular terms, are exactly the ones that are the unique models of monadic second-order sentences.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:02:15 +0000</pubDate>
      <link>https://fi.episciences.org/8964</link>
      <guid>https://fi.episciences.org/8964</guid>
      <author>Courcelle, Bruno</author>
      <dc:creator>Courcelle, Bruno</dc:creator>
      <content:encoded><![CDATA[An order-theoretic forest is a countable partial order such that the set of elements larger than any element is linearly ordered. It is an order-theoretic tree if any two elements have an upper-bound. The order type of a branch can be any countable linear order. Such generalized infinite trees yield convenient definitions of the rank-width and the modular decomposition of countable graphs. We define an algebra based on only four operations that generate up to isomorphism and via infinite terms these order-theoretic trees and forests. We prove that the associated regular objects, those defined by regular terms, are exactly the ones that are the unique models of monadic second-order sentences.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Solving Infinite Games in the Baire Space</title>
      <description><![CDATA[Infinite games (in the form of Gale-Stewart games) are studied where a play is a sequence of natural numbers chosen by two players in alternation, the winning condition being a subset of the Baire space $\omega^\omega$. We consider such games defined by a natural kind of parity automata over the alphabet $\mathbb{N}$, called $\mathbb{N}$-MSO-automata, where transitions are specified by monadic second-order formulas over the successor structure of the natural numbers. We show that the classical B\"uchi-Landweber Theorem (for finite-state games in the Cantor space $2^\omega$) holds again for the present games: A game defined by a deterministic parity $\mathbb{N}$-MSO-automaton is determined, the winner can be computed, and an $\mathbb{N}$-MSO-transducer realizing a winning strategy for the winner can be constructed.]]></description>
      <pubDate>Fri, 21 Oct 2022 20:01:52 +0000</pubDate>
      <link>https://fi.episciences.org/9970</link>
      <guid>https://fi.episciences.org/9970</guid>
      <author>Brütsch, Benedikt</author>
      <author>Thomas, Wolfgang</author>
      <dc:creator>Brütsch, Benedikt</dc:creator>
      <dc:creator>Thomas, Wolfgang</dc:creator>
      <content:encoded><![CDATA[Infinite games (in the form of Gale-Stewart games) are studied where a play is a sequence of natural numbers chosen by two players in alternation, the winning condition being a subset of the Baire space $\omega^\omega$. We consider such games defined by a natural kind of parity automata over the alphabet $\mathbb{N}$, called $\mathbb{N}$-MSO-automata, where transitions are specified by monadic second-order formulas over the successor structure of the natural numbers. We show that the classical B\"uchi-Landweber Theorem (for finite-state games in the Cantor space $2^\omega$) holds again for the present games: A game defined by a deterministic parity $\mathbb{N}$-MSO-automaton is determined, the winner can be computed, and an $\mathbb{N}$-MSO-transducer realizing a winning strategy for the winner can be constructed.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Affine completeness of some free binary algebras</title>
      <description><![CDATA[A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. An algebra is said to be affine complete if every congruence preserving function is a polynomial function. We show that the algebra of (possibly empty) binary trees whose leaves are labeled by letters of an alphabet containing at least one letter, and the free monoid on an alphabet containing at least two letters are affine complete.]]></description>
      <pubDate>Fri, 21 Oct 2022 19:58:02 +0000</pubDate>
      <link>https://fi.episciences.org/8962</link>
      <guid>https://fi.episciences.org/8962</guid>
      <author>Arnold, André</author>
      <author>Cégielski, Patrick</author>
      <author>Guessarian, Irène</author>
      <dc:creator>Arnold, André</dc:creator>
      <dc:creator>Cégielski, Patrick</dc:creator>
      <dc:creator>Guessarian, Irène</dc:creator>
      <content:encoded><![CDATA[A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. An algebra is said to be affine complete if every congruence preserving function is a polynomial function. We show that the algebra of (possibly empty) binary trees whose leaves are labeled by letters of an alphabet containing at least one letter, and the free monoid on an alphabet containing at least two letters are affine complete.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Structure and Power: an emerging landscape</title>
      <description><![CDATA[In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer Science, but there may also be something of interest for model theorists and other logicians. The basic setting involves studying the category of relational structures via a resource-indexed family of adjunctions with some process category - which unfolds relational structures into treelike forms, allowing natural resource parameters to be assigned to these unfoldings. One basic instance of this scheme allows us to recover, in a purely structural, syntax-free way: the Ehrenfeucht-Fraisse~game; the quantifier rank fragments of first-order logic; the equivalences on structures induced by (i) the quantifier rank fragments, (ii) the restriction of this fragment to the existential positive part, and (iii) the extension with counting quantifiers; and the combinatorial parameter of tree-depth (Nesetril and Ossona de Mendez). Another instance recovers the k-pebble game, the finite-variable fragments, the corresponding equivalences, and the combinatorial parameter of treewidth. Other instances cover modal, guarded and hybrid fragments, generalized quantifiers, and a wide range of combinatorial parameters. This whole scheme has been axiomatized in a very general setting, of arboreal categories and arboreal covers. Beyond this basic level, a landscape is beginning to emerge, in which structural features of the resource categories, adjunctions and comonads are reflected in degrees of logical and computational tractability of the corresponding languages. Examples include semantic characterisation and preservation theorems, and Lovasz-type results on counting homomorphisms.]]></description>
      <pubDate>Fri, 21 Oct 2022 19:57:10 +0000</pubDate>
      <link>https://fi.episciences.org/9995</link>
      <guid>https://fi.episciences.org/9995</guid>
      <author>Abramsky, Samson</author>
      <dc:creator>Abramsky, Samson</dc:creator>
      <content:encoded><![CDATA[In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer Science, but there may also be something of interest for model theorists and other logicians. The basic setting involves studying the category of relational structures via a resource-indexed family of adjunctions with some process category - which unfolds relational structures into treelike forms, allowing natural resource parameters to be assigned to these unfoldings. One basic instance of this scheme allows us to recover, in a purely structural, syntax-free way: the Ehrenfeucht-Fraisse~game; the quantifier rank fragments of first-order logic; the equivalences on structures induced by (i) the quantifier rank fragments, (ii) the restriction of this fragment to the existential positive part, and (iii) the extension with counting quantifiers; and the combinatorial parameter of tree-depth (Nesetril and Ossona de Mendez). Another instance recovers the k-pebble game, the finite-variable fragments, the corresponding equivalences, and the combinatorial parameter of treewidth. Other instances cover modal, guarded and hybrid fragments, generalized quantifiers, and a wide range of combinatorial parameters. This whole scheme has been axiomatized in a very general setting, of arboreal categories and arboreal covers. Beyond this basic level, a landscape is beginning to emerge, in which structural features of the resource categories, adjunctions and comonads are reflected in degrees of logical and computational tractability of the corresponding languages. Examples include semantic characterisation and preservation theorems, and Lovasz-type results on counting homomorphisms.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On Random Number Generation for Kernel Applications</title>
      <description><![CDATA[An operating system kernel uses cryptographically secure pseudorandom number generator for creating address space localization randomization offsets to protect memory addresses to processes from exploration, storing users' password securely and creating cryptographic keys. The paper proposes a CSPRNG called KCS-PRNG which produces non-reproducible bitstreams. The proposed KCS-PRNG presents an efficient design uniquely configured with two new non-standard and verified elliptic curves and clock-controlled linear feedback shift registers and a novel method to consistently generate non-reproducible random bits of arbitrary lengths. The generated bit streams are statistically indistinguishable from true random bitstreams and provably secure, resilient to important attacks, exhibits backward and forward secrecy, exhibits exponential linear complexity, large period and huge key space.]]></description>
      <pubDate>Thu, 07 Jul 2022 10:20:00 +0000</pubDate>
      <link>https://fi.episciences.org/9650</link>
      <guid>https://fi.episciences.org/9650</guid>
      <author>Abhishek, Kunal</author>
      <author>E, George Dharma Prakash Raj</author>
      <dc:creator>Abhishek, Kunal</dc:creator>
      <dc:creator>E, George Dharma Prakash Raj</dc:creator>
      <content:encoded><![CDATA[An operating system kernel uses cryptographically secure pseudorandom number generator for creating address space localization randomization offsets to protect memory addresses to processes from exploration, storing users' password securely and creating cryptographic keys. The paper proposes a CSPRNG called KCS-PRNG which produces non-reproducible bitstreams. The proposed KCS-PRNG presents an efficient design uniquely configured with two new non-standard and verified elliptic curves and clock-controlled linear feedback shift registers and a novel method to consistently generate non-reproducible random bits of arbitrary lengths. The generated bit streams are statistically indistinguishable from true random bitstreams and provably secure, resilient to important attacks, exhibits backward and forward secrecy, exhibits exponential linear complexity, large period and huge key space.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Computational and Descriptional Power of Nondeterministic Iterated Uniform Finite-State Transducers</title>
      <description><![CDATA[An iterated uniform finite-state transducer (IUFST) runs the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The IUFST accepts the input string by halting in an accepting state at the end of a sweep. We consider both the deterministic (IUFST) and nondeterministic (NIUFST) version of this device. We show that constant sweep bounded IUFSTs and NIUFSTs accept all and only regular languages. We study the state complexity of removing nondeterminism as well as sweeps on constant sweep bounded NIUFSTs, the descriptional power of constant sweep bounded IUFSTs and NIUFSTs with respect to classical models of finite-state automata, and the computational complexity of several decidability questions. Then, we focus on non-constant sweep bounded devices, proving the existence of a proper infinite nonregular language hierarchy depending on the sweep complexity both in the deterministic and nondeterministic case. Though NIUFSTss are "one-way" devices we show that they characterize the class of context-sensitive languages, that is, the complexity class DSpace(lin). Finally, we show that the nondeterministic devices are more powerful than their deterministic variant for a sublinear number of sweeps that is at least logarithmic.]]></description>
      <pubDate>Thu, 07 Jul 2022 10:19:45 +0000</pubDate>
      <link>https://fi.episciences.org/9656</link>
      <guid>https://fi.episciences.org/9656</guid>
      <author>Kutrib, Martin</author>
      <author>Malcher, Andreas</author>
      <author>Mereghetti, Carlo</author>
      <author>Palano, Beatrice</author>
      <dc:creator>Kutrib, Martin</dc:creator>
      <dc:creator>Malcher, Andreas</dc:creator>
      <dc:creator>Mereghetti, Carlo</dc:creator>
      <dc:creator>Palano, Beatrice</dc:creator>
      <content:encoded><![CDATA[An iterated uniform finite-state transducer (IUFST) runs the same length-preserving transduction, starting with a sweep on the input string and then iteratively sweeping on the output of the previous sweep. The IUFST accepts the input string by halting in an accepting state at the end of a sweep. We consider both the deterministic (IUFST) and nondeterministic (NIUFST) version of this device. We show that constant sweep bounded IUFSTs and NIUFSTs accept all and only regular languages. We study the state complexity of removing nondeterminism as well as sweeps on constant sweep bounded NIUFSTs, the descriptional power of constant sweep bounded IUFSTs and NIUFSTs with respect to classical models of finite-state automata, and the computational complexity of several decidability questions. Then, we focus on non-constant sweep bounded devices, proving the existence of a proper infinite nonregular language hierarchy depending on the sweep complexity both in the deterministic and nondeterministic case. Though NIUFSTss are "one-way" devices we show that they characterize the class of context-sensitive languages, that is, the complexity class DSpace(lin). Finally, we show that the nondeterministic devices are more powerful than their deterministic variant for a sublinear number of sweeps that is at least logarithmic.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A Local Diagnosis Algorithm for Hypercube-like Networks under the BGM Diagnosis Model</title>
      <description><![CDATA[System diagnosis is process of identifying faulty nodes in a system. An efficient diagnosis is crucial for a multiprocessor system. The BGM diagnosis model is a modification of the PMC diagnosis model, which is a test-based diagnosis. In this paper, we present a specific structure and propose an algorithm for diagnosing a node in a system under the BGM model. We also give a polynomial-time algorithm that a node in a hypercube-like network can be diagnosed correctly in three test rounds under the BGM diagnosis model.]]></description>
      <pubDate>Thu, 07 Jul 2022 10:19:28 +0000</pubDate>
      <link>https://fi.episciences.org/9668</link>
      <guid>https://fi.episciences.org/9668</guid>
      <author>Lin, Cheng-Kuan</author>
      <author>Kung, Tzu-Liang</author>
      <author>Hung, Chun-Nan</author>
      <author>Teng, Yuan-Hsiang</author>
      <dc:creator>Lin, Cheng-Kuan</dc:creator>
      <dc:creator>Kung, Tzu-Liang</dc:creator>
      <dc:creator>Hung, Chun-Nan</dc:creator>
      <dc:creator>Teng, Yuan-Hsiang</dc:creator>
      <content:encoded><![CDATA[System diagnosis is process of identifying faulty nodes in a system. An efficient diagnosis is crucial for a multiprocessor system. The BGM diagnosis model is a modification of the PMC diagnosis model, which is a test-based diagnosis. In this paper, we present a specific structure and propose an algorithm for diagnosing a node in a system under the BGM model. We also give a polynomial-time algorithm that a node in a hypercube-like network can be diagnosed correctly in three test rounds under the BGM diagnosis model.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Characteristics of de Bruijn's early proof checker Automath</title>
      <description><![CDATA[The `mathematical language' Automath, conceived by N.G. de Bruijn in 1968, was the first theorem prover actually working and was used for checking many specimina of mathematical content. Its goals and syntactic ideas inspired Th. Coquand and G. Huet to develop the calculus of constructions, CC, which was one of the first widely used interactive theorem provers and forms the basis for the widely used Coq system. The original syntax of Automath is not easy to grasp. Yet, it is essentially based on a derivation system that is similar to the Calculus of Constructions (`CC'). The relation between the Automath syntax and CC has not yet been sufficiently described, although there are many references in the type theory community to Automath. In this paper we focus on the backgrounds and on some uncommon aspects of the syntax of Automath. We expose the fundamental aspects of a `generic' Automath system, encapsulating the most common versions of Automath. We present this generic Automath system in a modern syntactic frame. The obtained system makes use of {\lambda}D, a direct extension of CC with definitions.]]></description>
      <pubDate>Thu, 07 Jul 2022 10:19:01 +0000</pubDate>
      <link>https://fi.episciences.org/9711</link>
      <guid>https://fi.episciences.org/9711</guid>
      <author>Geuvers, Herman</author>
      <author>Nederpelt, Rob</author>
      <dc:creator>Geuvers, Herman</dc:creator>
      <dc:creator>Nederpelt, Rob</dc:creator>
      <content:encoded><![CDATA[The `mathematical language' Automath, conceived by N.G. de Bruijn in 1968, was the first theorem prover actually working and was used for checking many specimina of mathematical content. Its goals and syntactic ideas inspired Th. Coquand and G. Huet to develop the calculus of constructions, CC, which was one of the first widely used interactive theorem provers and forms the basis for the widely used Coq system. The original syntax of Automath is not easy to grasp. Yet, it is essentially based on a derivation system that is similar to the Calculus of Constructions (`CC'). The relation between the Automath syntax and CC has not yet been sufficiently described, although there are many references in the type theory community to Automath. In this paper we focus on the backgrounds and on some uncommon aspects of the syntax of Automath. We expose the fundamental aspects of a `generic' Automath system, encapsulating the most common versions of Automath. We present this generic Automath system in a modern syntactic frame. The obtained system makes use of {\lambda}D, a direct extension of CC with definitions.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Nominal Unification and Matching of Higher Order Expressions with Recursive Let</title>
      <description><![CDATA[A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in nondeterministic polynomial time. We also explore specializations like nominal letrec-matching for expressions, for DAGs, and for garbage-free expressions and determine their complexity. We also provide a nominal unification algorithm for higher-order expressions with recursive let and atom-variables, where we show that it also runs in nondeterministic polynomial time. In addition we prove that there is a guessing strategy for nominal unification with letrec and atom-variable that is a trade-off between exponential growth and non-determinism. Nominal matching with variables representing partial letrec-environments is also shown to be in NP.]]></description>
      <pubDate>Fri, 06 May 2022 17:44:07 +0000</pubDate>
      <link>https://fi.episciences.org/9393</link>
      <guid>https://fi.episciences.org/9393</guid>
      <author>Schmidt-Schauß, Manfred</author>
      <author>Kutsia, Temur</author>
      <author>Levy, Jordi</author>
      <author>Villaret, Mateu</author>
      <author>Kutz, Yunus</author>
      <dc:creator>Schmidt-Schauß, Manfred</dc:creator>
      <dc:creator>Kutsia, Temur</dc:creator>
      <dc:creator>Levy, Jordi</dc:creator>
      <dc:creator>Villaret, Mateu</dc:creator>
      <dc:creator>Kutz, Yunus</dc:creator>
      <content:encoded><![CDATA[A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in nondeterministic polynomial time. We also explore specializations like nominal letrec-matching for expressions, for DAGs, and for garbage-free expressions and determine their complexity. We also provide a nominal unification algorithm for higher-order expressions with recursive let and atom-variables, where we show that it also runs in nondeterministic polynomial time. In addition we prove that there is a guessing strategy for nominal unification with letrec and atom-variable that is a trade-off between exponential growth and non-determinism. Nominal matching with variables representing partial letrec-environments is also shown to be in NP.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Coxeter invariants for non-negative unit forms of Dynkin type A</title>
      <description><![CDATA[Two integral quadratic unit forms are called strongly Gram congruent if their upper triangular Gram matrices are Z-congruent. The paper gives a combinatorial strong Gram invariant for those unit forms that are non-negative of Dynkin type A, within the framework introduced in [Fundamenta Informaticae 184(1):49-82, 2021], and uses it to determine all corresponding Coxeter polynomials and (reduced) Coxeter numbers.]]></description>
      <pubDate>Fri, 06 May 2022 17:43:44 +0000</pubDate>
      <link>https://fi.episciences.org/9391</link>
      <guid>https://fi.episciences.org/9391</guid>
      <author>González, Jesús Arturo Jiménez</author>
      <dc:creator>González, Jesús Arturo Jiménez</dc:creator>
      <content:encoded><![CDATA[Two integral quadratic unit forms are called strongly Gram congruent if their upper triangular Gram matrices are Z-congruent. The paper gives a combinatorial strong Gram invariant for those unit forms that are non-negative of Dynkin type A, within the framework introduced in [Fundamenta Informaticae 184(1):49-82, 2021], and uses it to determine all corresponding Coxeter polynomials and (reduced) Coxeter numbers.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Perfect domination, Roman domination and perfect Roman domination in lexicographic product graphs</title>
      <description><![CDATA[The aim of this paper is to obtain closed formulas for the perfect domination number, the Roman domination number and the perfect Roman domination number of lexicographic product graphs. We show that these formulas can be obtained relatively easily for the case of the first two parameters. The picture is quite different when it concerns the perfect Roman domination number. In this case, we obtain general bounds and then we give sufficient and/or necessary conditions for the bounds to be achieved. We also discuss the case of perfect Roman graphs and we characterize the lexicographic product graphs where the perfect Roman domination number equals the Roman domination number.]]></description>
      <pubDate>Fri, 06 May 2022 17:43:27 +0000</pubDate>
      <link>https://fi.episciences.org/9395</link>
      <guid>https://fi.episciences.org/9395</guid>
      <author>Martinez, A. Cabrera</author>
      <author>Garcia-Gomez, C.</author>
      <author>Rodriguez-Velazquez, J. A.</author>
      <dc:creator>Martinez, A. Cabrera</dc:creator>
      <dc:creator>Garcia-Gomez, C.</dc:creator>
      <dc:creator>Rodriguez-Velazquez, J. A.</dc:creator>
      <content:encoded><![CDATA[The aim of this paper is to obtain closed formulas for the perfect domination number, the Roman domination number and the perfect Roman domination number of lexicographic product graphs. We show that these formulas can be obtained relatively easily for the case of the first two parameters. The picture is quite different when it concerns the perfect Roman domination number. In this case, we obtain general bounds and then we give sufficient and/or necessary conditions for the bounds to be achieved. We also discuss the case of perfect Roman graphs and we characterize the lexicographic product graphs where the perfect Roman domination number equals the Roman domination number.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On the $2$-domination number of cylinders with small cycles</title>
      <description><![CDATA[Domination-type parameters are difficult to manage in Cartesian product graphs and there is usually no general relationship between the parameter in both factors and in the product graph. This is the situation of the domination number, the Roman domination number or the $2$-domination number, among others. Contrary to what happens with the domination number and the Roman domination number, the $2$-domination number remains unknown in cylinders, that is, the Cartesian product of a cycle and a path and in this paper, we will compute this parameter in the cylinders with small cycles. We will develop two algorithms involving the $(\min,+)$ matrix product that will allow us to compute the desired values of $\gamma_2(C_n\Box P_m)$, with $3\leq n\leq 15$ and $m\geq 2$. We will also pose a conjecture about the general formulae for the $2$-domination number in this graph class.]]></description>
      <pubDate>Fri, 06 May 2022 17:42:59 +0000</pubDate>
      <link>https://fi.episciences.org/9353</link>
      <guid>https://fi.episciences.org/9353</guid>
      <author>Garzón, E. M.</author>
      <author>Martínez, J. A.</author>
      <author>Moreno, J. J.</author>
      <author>Puertas, M. L.</author>
      <dc:creator>Garzón, E. M.</dc:creator>
      <dc:creator>Martínez, J. A.</dc:creator>
      <dc:creator>Moreno, J. J.</dc:creator>
      <dc:creator>Puertas, M. L.</dc:creator>
      <content:encoded><![CDATA[Domination-type parameters are difficult to manage in Cartesian product graphs and there is usually no general relationship between the parameter in both factors and in the product graph. This is the situation of the domination number, the Roman domination number or the $2$-domination number, among others. Contrary to what happens with the domination number and the Roman domination number, the $2$-domination number remains unknown in cylinders, that is, the Cartesian product of a cycle and a path and in this paper, we will compute this parameter in the cylinders with small cycles. We will develop two algorithms involving the $(\min,+)$ matrix product that will allow us to compute the desired values of $\gamma_2(C_n\Box P_m)$, with $3\leq n\leq 15$ and $m\geq 2$. We will also pose a conjecture about the general formulae for the $2$-domination number in this graph class.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Getting There and Back Again</title>
      <description><![CDATA["There and Back Again" (TABA) is a programming pattern where the recursive calls traverse one data structure and the subsequent returns traverse another. This article presents new TABA examples, refines existing ones, and formalizes both their control flow and their data flow using the Coq Proof Assistant. Each formalization mechanizes a pen-and-paper proof, thus making it easier to "get" TABA. In addition, this article identifies and illustrates a tail-recursive variant of TABA, There and Forth Again (TAFA) that does not come back but goes forth instead with more tail calls.]]></description>
      <pubDate>Fri, 06 May 2022 17:42:38 +0000</pubDate>
      <link>https://fi.episciences.org/9356</link>
      <guid>https://fi.episciences.org/9356</guid>
      <author>Danvy, Olivier</author>
      <dc:creator>Danvy, Olivier</dc:creator>
      <content:encoded><![CDATA["There and Back Again" (TABA) is a programming pattern where the recursive calls traverse one data structure and the subsequent returns traverse another. This article presents new TABA examples, refines existing ones, and formalizes both their control flow and their data flow using the Coq Proof Assistant. Each formalization mechanizes a pen-and-paper proof, thus making it easier to "get" TABA. In addition, this article identifies and illustrates a tail-recursive variant of TABA, There and Forth Again (TAFA) that does not come back but goes forth instead with more tail calls.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On local antimagic vertex coloring for complete full $t$-ary trees</title>
      <description><![CDATA[Let $G = (V, E)$ be a finite simple undirected graph without $K_2$ components. A bijection $f : E \rightarrow \{1, 2,\cdots, |E|\}$ is called a local antimagic labeling if for any two adjacent vertices $u$ and $v$, they have different vertex sums, i.e., $w(u) \neq w(v)$, where the vertex sum $w(u) = \sum_{e \in E(u)} f(e)$, and $E(u)$ is the set of edges incident to $u$. Thus any local antimagic labeling induces a proper vertex coloring of $G$ where the vertex $v$ is assigned the color (vertex sum) $w(v)$. The local antimagic chromatic number $\chi_{la}(G)$ is the minimum number of colors taken over all colorings induced by local antimagic labelings of $G$. It was conjectured \cite{Aru-Wang} that for every tree $T$ the local antimagic chromatic number $l+ 1 \leq \chi_{la} ( T )\leq l+2$, where $l$ is the number of leaves of $T$. In this article we verify the above conjecture for complete full $t$-ary trees, for $t \geq 2$. A complete full $t$-ary tree is a rooted tree in which all nodes have exactly $t$ children except leaves and every leaf is of the same depth. In particular we obtain that the exact value for the local antimagic chromatic number of all complete full $t$-ary trees is $ l+1$ for odd $t$.]]></description>
      <pubDate>Fri, 06 May 2022 17:42:16 +0000</pubDate>
      <link>https://fi.episciences.org/9349</link>
      <guid>https://fi.episciences.org/9349</guid>
      <author>Bača, Martin</author>
      <author>Semaničová-Feňovčíková, Andrea</author>
      <author>Lai, Ruei-Ting</author>
      <author>Wang, Tao-Ming</author>
      <dc:creator>Bača, Martin</dc:creator>
      <dc:creator>Semaničová-Feňovčíková, Andrea</dc:creator>
      <dc:creator>Lai, Ruei-Ting</dc:creator>
      <dc:creator>Wang, Tao-Ming</dc:creator>
      <content:encoded><![CDATA[Let $G = (V, E)$ be a finite simple undirected graph without $K_2$ components. A bijection $f : E \rightarrow \{1, 2,\cdots, |E|\}$ is called a local antimagic labeling if for any two adjacent vertices $u$ and $v$, they have different vertex sums, i.e., $w(u) \neq w(v)$, where the vertex sum $w(u) = \sum_{e \in E(u)} f(e)$, and $E(u)$ is the set of edges incident to $u$. Thus any local antimagic labeling induces a proper vertex coloring of $G$ where the vertex $v$ is assigned the color (vertex sum) $w(v)$. The local antimagic chromatic number $\chi_{la}(G)$ is the minimum number of colors taken over all colorings induced by local antimagic labelings of $G$. It was conjectured \cite{Aru-Wang} that for every tree $T$ the local antimagic chromatic number $l+ 1 \leq \chi_{la} ( T )\leq l+2$, where $l$ is the number of leaves of $T$. In this article we verify the above conjecture for complete full $t$-ary trees, for $t \geq 2$. A complete full $t$-ary tree is a rooted tree in which all nodes have exactly $t$ children except leaves and every leaf is of the same depth. In particular we obtain that the exact value for the local antimagic chromatic number of all complete full $t$-ary trees is $ l+1$ for odd $t$.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Spanning Structures in Walker--Breaker Games</title>
      <description><![CDATA[We study the biased $(2:b)$ Walker--Breaker games, played on the edge set of the complete graph on $n$ vertices, $K_n$. These games are a variant of the Maker--Breaker games with the restriction that Walker (playing the role of Maker) has to choose her edges according to a walk. We look at the two standard graph games -- the Connectivity game and the Hamilton Cycle game and show that Walker can win both games even when playing against Breaker whose bias is of the order of magnitude $n/ \ln n$.]]></description>
      <pubDate>Thu, 10 Mar 2022 10:44:19 +0000</pubDate>
      <link>https://fi.episciences.org/9185</link>
      <guid>https://fi.episciences.org/9185</guid>
      <author>Forcan, Jovana</author>
      <author>Mikalački, Mirjana</author>
      <dc:creator>Forcan, Jovana</dc:creator>
      <dc:creator>Mikalački, Mirjana</dc:creator>
      <content:encoded><![CDATA[We study the biased $(2:b)$ Walker--Breaker games, played on the edge set of the complete graph on $n$ vertices, $K_n$. These games are a variant of the Maker--Breaker games with the restriction that Walker (playing the role of Maker) has to choose her edges according to a walk. We look at the two standard graph games -- the Connectivity game and the Hamilton Cycle game and show that Walker can win both games even when playing against Breaker whose bias is of the order of magnitude $n/ \ln n$.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Self-stabilisation of cellular automata on tilings</title>
      <description><![CDATA[Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a valid configuration, the cellular automaton must eventually fall back into the space of valid configurations where it remains still. We allow the cellular automaton to use extra symbols, but in that case, the extra symbols can also appear in the initial finite perturbation. For several classes of local constraints (e.g., $k$-colourings with $k\neq 3$, and North-East deterministic constraints), we provide efficient self-stabilising cellular automata with or without additional symbols that wash out finite perturbations in linear or quadratic time, but also show that there are examples of local constraints for which the self-stabilisation problem is inherently hard. We note that the optimal self-stabilisation speed is the same for all local constraints that are isomorphic to one another. We also consider probabilistic cellular automata rules and show that in some cases, the use of randomness simplifies the problem. In the deterministic case, we show that if finite perturbations are corrected in linear time, then the cellular automaton self-stabilises even starting from a random perturbation of a valid configuration, that is, when errors in the initial configuration occur independently with a sufficiently low density.]]></description>
      <pubDate>Thu, 10 Mar 2022 10:43:54 +0000</pubDate>
      <link>https://fi.episciences.org/9184</link>
      <guid>https://fi.episciences.org/9184</guid>
      <author>Fatès, Nazim</author>
      <author>Marcovici, Irène</author>
      <author>Taati, Siamak</author>
      <dc:creator>Fatès, Nazim</dc:creator>
      <dc:creator>Marcovici, Irène</dc:creator>
      <dc:creator>Taati, Siamak</dc:creator>
      <content:encoded><![CDATA[Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a valid configuration, the cellular automaton must eventually fall back into the space of valid configurations where it remains still. We allow the cellular automaton to use extra symbols, but in that case, the extra symbols can also appear in the initial finite perturbation. For several classes of local constraints (e.g., $k$-colourings with $k\neq 3$, and North-East deterministic constraints), we provide efficient self-stabilising cellular automata with or without additional symbols that wash out finite perturbations in linear or quadratic time, but also show that there are examples of local constraints for which the self-stabilisation problem is inherently hard. We note that the optimal self-stabilisation speed is the same for all local constraints that are isomorphic to one another. We also consider probabilistic cellular automata rules and show that in some cases, the use of randomness simplifies the problem. In the deterministic case, we show that if finite perturbations are corrected in linear time, then the cellular automaton self-stabilises even starting from a random perturbation of a valid configuration, that is, when errors in the initial configuration occur independently with a sufficiently low density.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On morphisms preserving palindromic richness</title>
      <description><![CDATA[It is known that each word of length $n$ contains at most $n+1$ distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite words. Sturmian words and Rote complementary symmetric sequences form two classes of binary rich words, while episturmian words and words coding symmetric $d$-interval exchange transformations give us other examples on larger alphabets. In this paper we look for morphisms of the free monoid, which allow us to construct new rich words from already known rich words. We focus on morphisms in Class $P_{ret}$. This class contains morphisms injective on the alphabet and satisfying a particular palindromicity property: for every morphism $\varphi$ in the class there exists a palindrome $w$ such that $\varphi(a)w$ is a first complete return word to $w$ for each letter $a$. We characterize $P_{ret}$ morphisms which preserve richness over a binary alphabet. We also study marked $P_{ret}$ morphisms acting on alphabets with more letters. In particular we show that every Arnoux-Rauzy morphism is conjugated to a morphism in Class $P_{ret}$ and that it preserves richness.]]></description>
      <pubDate>Thu, 10 Mar 2022 10:43:35 +0000</pubDate>
      <link>https://fi.episciences.org/9182</link>
      <guid>https://fi.episciences.org/9182</guid>
      <author>Dolce, Francesco</author>
      <author>Pelantová, Edita</author>
      <dc:creator>Dolce, Francesco</dc:creator>
      <dc:creator>Pelantová, Edita</dc:creator>
      <content:encoded><![CDATA[It is known that each word of length $n$ contains at most $n+1$ distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of palindromic richness can be naturally extended to infinite words. Sturmian words and Rote complementary symmetric sequences form two classes of binary rich words, while episturmian words and words coding symmetric $d$-interval exchange transformations give us other examples on larger alphabets. In this paper we look for morphisms of the free monoid, which allow us to construct new rich words from already known rich words. We focus on morphisms in Class $P_{ret}$. This class contains morphisms injective on the alphabet and satisfying a particular palindromicity property: for every morphism $\varphi$ in the class there exists a palindrome $w$ such that $\varphi(a)w$ is a first complete return word to $w$ for each letter $a$. We characterize $P_{ret}$ morphisms which preserve richness over a binary alphabet. We also study marked $P_{ret}$ morphisms acting on alphabets with more letters. In particular we show that every Arnoux-Rauzy morphism is conjugated to a morphism in Class $P_{ret}$ and that it preserves richness.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A polynomial-time construction of a hitting set for read-once branching programs of width 3</title>
      <description><![CDATA[Recently, an interest in constructing pseudorandom or hitting set generators for restricted branching programs has increased, which is motivated by the fundamental issue of derandomizing space-bounded computations. Such constructions have been known only in the case of width 2 and in very restricted cases of bounded width. In this paper, we characterize the hitting sets for read-once branching programs of width 3 by a so-called richness condition. Namely, we show that such sets hit the class of read-once conjunctions of DNF and CNF (i.e. the weak richness). Moreover, we prove that any rich set extended with all strings within Hamming distance of 3 is a hitting set for read-once branching programs of width 3. Then, we show that any almost $O(\log n)$-wise independent set satisfies the richness condition. By using such a set due to Alon et al. (1992) our result provides an explicit polynomial-time construction of a hitting set for read-once branching programs of width 3 with acceptance probability $\varepsilon>5/6$. We announced this result at conferences more than ten years ago, including only proof sketches, which motivated a number of subsequent results on pseudorandom generators for restricted read-once branching programs. This paper contains our original detailed proof that has not been published yet.]]></description>
      <pubDate>Thu, 10 Mar 2022 10:40:13 +0000</pubDate>
      <link>https://fi.episciences.org/9057</link>
      <guid>https://fi.episciences.org/9057</guid>
      <author>Šíma, Jiří</author>
      <author>Žák, Stanislav</author>
      <dc:creator>Šíma, Jiří</dc:creator>
      <dc:creator>Žák, Stanislav</dc:creator>
      <content:encoded><![CDATA[Recently, an interest in constructing pseudorandom or hitting set generators for restricted branching programs has increased, which is motivated by the fundamental issue of derandomizing space-bounded computations. Such constructions have been known only in the case of width 2 and in very restricted cases of bounded width. In this paper, we characterize the hitting sets for read-once branching programs of width 3 by a so-called richness condition. Namely, we show that such sets hit the class of read-once conjunctions of DNF and CNF (i.e. the weak richness). Moreover, we prove that any rich set extended with all strings within Hamming distance of 3 is a hitting set for read-once branching programs of width 3. Then, we show that any almost $O(\log n)$-wise independent set satisfies the richness condition. By using such a set due to Alon et al. (1992) our result provides an explicit polynomial-time construction of a hitting set for read-once branching programs of width 3 with acceptance probability $\varepsilon>5/6$. We announced this result at conferences more than ten years ago, including only proof sketches, which motivated a number of subsequent results on pseudorandom generators for restricted read-once branching programs. This paper contains our original detailed proof that has not been published yet.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Computing the Length of Sum of Squares and Pythagoras Element in a Global Field</title>
      <description><![CDATA[This paper presents algorithms for computing the length of a sum of squares and a Pythagoras element in a global field $K$ of characteristic different from $2$. In the first part of the paper, we present algorithms for computing the length in a non-dyadic and dyadic (if $K$ is a number field) completion of $K$. These two algorithms serve as subsidiary steps for computing lengths in global fields. In the second part of the paper we present a procedure for constructing an element whose length equals the Pythagoras number of a global field, termed a Pythagoras element.]]></description>
      <pubDate>Thu, 10 Mar 2022 10:39:53 +0000</pubDate>
      <link>https://fi.episciences.org/9068</link>
      <guid>https://fi.episciences.org/9068</guid>
      <author>Darkey-Mensah, Mawunyo Kofi</author>
      <author>Rothkegel, Beata</author>
      <dc:creator>Darkey-Mensah, Mawunyo Kofi</dc:creator>
      <dc:creator>Rothkegel, Beata</dc:creator>
      <content:encoded><![CDATA[This paper presents algorithms for computing the length of a sum of squares and a Pythagoras element in a global field $K$ of characteristic different from $2$. In the first part of the paper, we present algorithms for computing the length in a non-dyadic and dyadic (if $K$ is a number field) completion of $K$. These two algorithms serve as subsidiary steps for computing lengths in global fields. In the second part of the paper we present a procedure for constructing an element whose length equals the Pythagoras number of a global field, termed a Pythagoras element.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Acyclic and Cyclic Reversing Computations in Petri Nets</title>
      <description><![CDATA[Reversible computations constitute an unconventional form of computing where any sequence of performed operations can be undone by executing in reverse order at any point during a computation. It has been attracting increasing attention as it provides opportunities for low-power computation, being at the same time essential or eligible in various applications. In recent work, we have proposed a structural way of translating Reversing Petri Nets (RPNs) - a type of Petri nets that embeds reversible computation, to bounded Coloured Petri Nets (CPNs) - an extension of traditional Petri Nets, where tokens carry data values. Three reversing semantics are possible in RPNs: backtracking (reversing of the lately executed action), causal reversing (action can be reversed only when all its effects have been undone) and out of causal reversing (any previously performed action can be reversed). In this paper, we extend the RPN to CPN translation with formal proofs of correctness. Moreover, the possibility of introduction of cycles to RPNs is discussed. We analyze which type of cycles could be allowed in RPNs to ensure consistency with the current semantics. It emerged that the most interesting case related to cycles in RPNs occurs in causal semantics, where various interpretations of dependency result in different net's behaviour during reversing. Three definitions of dependence are presented and discussed.]]></description>
      <pubDate>Thu, 10 Mar 2022 10:39:30 +0000</pubDate>
      <link>https://fi.episciences.org/9073</link>
      <guid>https://fi.episciences.org/9073</guid>
      <author>Barylska, Kamila</author>
      <author>Gogolińska, Anna</author>
      <dc:creator>Barylska, Kamila</dc:creator>
      <dc:creator>Gogolińska, Anna</dc:creator>
      <content:encoded><![CDATA[Reversible computations constitute an unconventional form of computing where any sequence of performed operations can be undone by executing in reverse order at any point during a computation. It has been attracting increasing attention as it provides opportunities for low-power computation, being at the same time essential or eligible in various applications. In recent work, we have proposed a structural way of translating Reversing Petri Nets (RPNs) - a type of Petri nets that embeds reversible computation, to bounded Coloured Petri Nets (CPNs) - an extension of traditional Petri Nets, where tokens carry data values. Three reversing semantics are possible in RPNs: backtracking (reversing of the lately executed action), causal reversing (action can be reversed only when all its effects have been undone) and out of causal reversing (any previously performed action can be reversed). In this paper, we extend the RPN to CPN translation with formal proofs of correctness. Moreover, the possibility of introduction of cycles to RPNs is discussed. We analyze which type of cycles could be allowed in RPNs to ensure consistency with the current semantics. It emerged that the most interesting case related to cycles in RPNs occurs in causal semantics, where various interpretations of dependency result in different net's behaviour during reversing. Three definitions of dependence are presented and discussed.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Theory of constructive semigroups with apartness -- foundations, development and practice</title>
      <description><![CDATA[This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also draw attention to its possible applications in other (constructive) mathematics disciplines, in computer science, social sciences, economics, etc. Another important goal of this paper is to provide a clear, understandable picture of constructive semigroups with apartness in Bishop's style both to (classical) algebraists and the ones who apply algebraic knowledge.]]></description>
      <pubDate>Wed, 02 Feb 2022 19:52:56 +0000</pubDate>
      <link>https://fi.episciences.org/9009</link>
      <guid>https://fi.episciences.org/9009</guid>
      <author>Mitrovic, Melanija</author>
      <author>Hounkonnou, Mahouton Norbert</author>
      <author>Baroni, Marian Alexandru</author>
      <dc:creator>Mitrovic, Melanija</dc:creator>
      <dc:creator>Hounkonnou, Mahouton Norbert</dc:creator>
      <dc:creator>Baroni, Marian Alexandru</dc:creator>
      <content:encoded><![CDATA[This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also draw attention to its possible applications in other (constructive) mathematics disciplines, in computer science, social sciences, economics, etc. Another important goal of this paper is to provide a clear, understandable picture of constructive semigroups with apartness in Bishop's style both to (classical) algebraists and the ones who apply algebraic knowledge.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On the Hardness of Energy Minimisation for Crystal Structure Prediction</title>
      <description><![CDATA[Crystal Structure Prediction (csp) is one of the central and most challenging problems in materials science and computational chemistry. In csp, the goal is to find a configuration of ions in 3D space that yields the lowest potential energy. Finding an efficient procedure to solve this complex optimisation question is a well known open problem. Due to the exponentially large search space, the problem has been referred in several materials-science papers as "NP-Hard and very challenging" without a formal proof. This paper fills a gap in the literature providing the first set of formally proven NP-Hardness results for a variant of csp with various realistic constraints. In particular, we focus on the problem of removal: the goal is to find a substructure with minimal potential energy, by removing a subset of the ions. Our main contributions are NP-Hardness results for the csp removal problem, new embeddings of combinatorial graph problems into geometrical settings, and a more systematic exploration of the energy function to reveal the complexity of csp. In a wider context, our results contribute to the analysis of computational problems for weighted graphs embedded into the three-dimensional Euclidean space.]]></description>
      <pubDate>Wed, 02 Feb 2022 19:52:30 +0000</pubDate>
      <link>https://fi.episciences.org/9010</link>
      <guid>https://fi.episciences.org/9010</guid>
      <author>Adamson, Duncan</author>
      <author>Deligkas, Argyrios</author>
      <author>Gusev, Vladimir</author>
      <author>Potapov, Igor</author>
      <dc:creator>Adamson, Duncan</dc:creator>
      <dc:creator>Deligkas, Argyrios</dc:creator>
      <dc:creator>Gusev, Vladimir</dc:creator>
      <dc:creator>Potapov, Igor</dc:creator>
      <content:encoded><![CDATA[Crystal Structure Prediction (csp) is one of the central and most challenging problems in materials science and computational chemistry. In csp, the goal is to find a configuration of ions in 3D space that yields the lowest potential energy. Finding an efficient procedure to solve this complex optimisation question is a well known open problem. Due to the exponentially large search space, the problem has been referred in several materials-science papers as "NP-Hard and very challenging" without a formal proof. This paper fills a gap in the literature providing the first set of formally proven NP-Hardness results for a variant of csp with various realistic constraints. In particular, we focus on the problem of removal: the goal is to find a substructure with minimal potential energy, by removing a subset of the ions. Our main contributions are NP-Hardness results for the csp removal problem, new embeddings of combinatorial graph problems into geometrical settings, and a more systematic exploration of the energy function to reveal the complexity of csp. In a wider context, our results contribute to the analysis of computational problems for weighted graphs embedded into the three-dimensional Euclidean space.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Clustering Geometrically-Modeled Points in the Aggregated Uncertainty Model</title>
      <description><![CDATA[The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the region-based uncertainty model, in which each $Q_i$ is an uncertain point, where the exact locations of the points in $Q_i$ are unknown. The geometric objects segments and polygons can be models of a point set. We define the uncertain version of the $k$-center problem as a generalization in which the objective is to find $k$ points from $Q$ to cover the remaining regions of $Q$ with minimum or maximum radius of the cluster to cover at least one or all exact instances of each $Q_i$, respectively. We modify the region-based model to allow multiple points to be chosen from a region and call the resulting model the aggregated uncertainty model. All these problems contain the point version as a special case, so they are all NP-hard with a lower bound 1.822. We give approximation algorithms for uncertain $k$-center of a set of segments and polygons. We also have implemented some of our algorithms on a data-set to show our theoretical performance guarantees can be achieved in practice.]]></description>
      <pubDate>Thu, 27 Jan 2022 11:35:22 +0000</pubDate>
      <link>https://fi.episciences.org/9005</link>
      <guid>https://fi.episciences.org/9005</guid>
      <author>Keikha, Vahideh</author>
      <author>Aghamolaei, Sepideh</author>
      <author>Mohades, Ali</author>
      <author>Ghodsi, Mohammad</author>
      <dc:creator>Keikha, Vahideh</dc:creator>
      <dc:creator>Aghamolaei, Sepideh</dc:creator>
      <dc:creator>Mohades, Ali</dc:creator>
      <dc:creator>Ghodsi, Mohammad</dc:creator>
      <content:encoded><![CDATA[The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the region-based uncertainty model, in which each $Q_i$ is an uncertain point, where the exact locations of the points in $Q_i$ are unknown. The geometric objects segments and polygons can be models of a point set. We define the uncertain version of the $k$-center problem as a generalization in which the objective is to find $k$ points from $Q$ to cover the remaining regions of $Q$ with minimum or maximum radius of the cluster to cover at least one or all exact instances of each $Q_i$, respectively. We modify the region-based model to allow multiple points to be chosen from a region and call the resulting model the aggregated uncertainty model. All these problems contain the point version as a special case, so they are all NP-hard with a lower bound 1.822. We give approximation algorithms for uncertain $k$-center of a set of segments and polygons. We also have implemented some of our algorithms on a data-set to show our theoretical performance guarantees can be achieved in practice.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>High-degree compression functions on alternative models of elliptic curves and their applications</title>
      <description><![CDATA[This paper presents method for obtaining high-degree compression functions using natural symmetries in a given model of an elliptic curve. Such symmetries may be found using symmetry of involution $[-1]$ and symmetry of translation morphism $\tau_T=P+T$, where $T$ is the $n$-torsion point which naturally belongs to the $E(\mathbb K)$ for a given elliptic curve model. We will study alternative models of elliptic curves with points of order $2$ and $4$, and specifically Huff's curves and the Hessian family of elliptic curves (like Hessian, twisted Hessian and generalized Hessian curves) with a point of order $3$. We bring up some known compression functions on those models and present new ones as well. For (almost) every presented compression function, differential addition and point doubling formulas are shown. As in the case of high-degree compression functions manual investigation of differential addition and doubling formulas is very difficult, we came up with a Magma program which relies on the Gr\"obner basis. We prove that if for a model $E$ of an elliptic curve exists an isomorphism $\phi:E \to E_M$, where $E_M$ is the Montgomery curve and for any $P \in E(\mathbb K)$ holds that $\phi(P)=(\phi_x(P), \phi_y(P))$, then for a model $E$ one may find compression function of degree $2$. Moreover, one may find, defined for this compression function, differential addition and doubling formulas of the same efficiency as Montgomery's. However, it seems that for the family of elliptic curves having a natural point of order $3$, compression functions of the same efficiency do not exist.]]></description>
      <pubDate>Thu, 27 Jan 2022 11:26:17 +0000</pubDate>
      <link>https://fi.episciences.org/8959</link>
      <guid>https://fi.episciences.org/8959</guid>
      <author>Wroński, Michał</author>
      <author>Kijko, Tomasz</author>
      <author>Dryło, Robert</author>
      <dc:creator>Wroński, Michał</dc:creator>
      <dc:creator>Kijko, Tomasz</dc:creator>
      <dc:creator>Dryło, Robert</dc:creator>
      <content:encoded><![CDATA[This paper presents method for obtaining high-degree compression functions using natural symmetries in a given model of an elliptic curve. Such symmetries may be found using symmetry of involution $[-1]$ and symmetry of translation morphism $\tau_T=P+T$, where $T$ is the $n$-torsion point which naturally belongs to the $E(\mathbb K)$ for a given elliptic curve model. We will study alternative models of elliptic curves with points of order $2$ and $4$, and specifically Huff's curves and the Hessian family of elliptic curves (like Hessian, twisted Hessian and generalized Hessian curves) with a point of order $3$. We bring up some known compression functions on those models and present new ones as well. For (almost) every presented compression function, differential addition and point doubling formulas are shown. As in the case of high-degree compression functions manual investigation of differential addition and doubling formulas is very difficult, we came up with a Magma program which relies on the Gr\"obner basis. We prove that if for a model $E$ of an elliptic curve exists an isomorphism $\phi:E \to E_M$, where $E_M$ is the Montgomery curve and for any $P \in E(\mathbb K)$ holds that $\phi(P)=(\phi_x(P), \phi_y(P))$, then for a model $E$ one may find compression function of degree $2$. Moreover, one may find, defined for this compression function, differential addition and doubling formulas of the same efficiency as Montgomery's. However, it seems that for the family of elliptic curves having a natural point of order $3$, compression functions of the same efficiency do not exist.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A Non-Deterministic Multiset Query Language</title>
      <description><![CDATA[We develop a multiset query and update language executable in a term rewriting system. Its most remarkable feature, besides non-standard approach to quantification and introduction of fresh values, is non-determinism - a query result is not uniquely determined by the database. We argue that this feature is very useful, e.g., in modelling user choices during simulation or reachability analysis of a data-centric business process - the intended application of our work. Query evaluation is implemented by converting the query into a terminating term rewriting system and normalizing the initial term which encapsulates the current database. A normal form encapsulates a query result. We prove that our language can express any relational algebra query. Finally, we present a simple business process specification framework (and an example specification). Both syntax and semantics of our query language is implemented in Maude.]]></description>
      <pubDate>Thu, 13 Jan 2022 08:41:46 +0000</pubDate>
      <link>https://fi.episciences.org/8950</link>
      <guid>https://fi.episciences.org/8950</guid>
      <author>Zielinski, Bartosz</author>
      <dc:creator>Zielinski, Bartosz</dc:creator>
      <content:encoded><![CDATA[We develop a multiset query and update language executable in a term rewriting system. Its most remarkable feature, besides non-standard approach to quantification and introduction of fresh values, is non-determinism - a query result is not uniquely determined by the database. We argue that this feature is very useful, e.g., in modelling user choices during simulation or reachability analysis of a data-centric business process - the intended application of our work. Query evaluation is implemented by converting the query into a terminating term rewriting system and normalizing the initial term which encapsulates the current database. A normal form encapsulates a query result. We prove that our language can express any relational algebra query. Finally, we present a simple business process specification framework (and an example specification). Both syntax and semantics of our query language is implemented in Maude.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Right Buchberger algorithm over bijective skew PBW extensions</title>
      <description><![CDATA[In this paper we present a right version of the algorithms developed for to compute Gr\"obner bases over bijective skew PBW extensions in the left case given in [3]. In particular, we adapt the theory of reduction and we build a right division algorithm and generate a right version of Buchberger algorithm over bijective skew PBW extensions, finally we illustrate some examples using the SPBWE.lib library implemented in Maple (see [1], [4]). It is important to note that the development of this theory is fundamental to complete the SPBWE.lib library and to be able to develop many of the homological applications that arise as result of obtaining the right Gr\"obner bases over skew PBW extensions.]]></description>
      <pubDate>Thu, 13 Jan 2022 08:41:18 +0000</pubDate>
      <link>https://fi.episciences.org/8949</link>
      <guid>https://fi.episciences.org/8949</guid>
      <author>Fajardo, W.</author>
      <dc:creator>Fajardo, W.</dc:creator>
      <content:encoded><![CDATA[In this paper we present a right version of the algorithms developed for to compute Gr\"obner bases over bijective skew PBW extensions in the left case given in [3]. In particular, we adapt the theory of reduction and we build a right division algorithm and generate a right version of Buchberger algorithm over bijective skew PBW extensions, finally we illustrate some examples using the SPBWE.lib library implemented in Maple (see [1], [4]). It is important to note that the development of this theory is fundamental to complete the SPBWE.lib library and to be able to develop many of the homological applications that arise as result of obtaining the right Gr\"obner bases over skew PBW extensions.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A graph theoretical framework for the strong Gram classification of non-negative unit forms of Dynkin type A</title>
      <description><![CDATA[In the context of signed line graphs, this article introduces a modified inflation technique to study strong Gram congruence of non-negative (integral quadratic) unit forms, and uses it to show that weak and strong Gram congruence coincide among positive unit forms of Dynkin type A. The concept of inverse of a quiver is also introduced, and is used to obtain and analyze the Coxeter matrix of non-negative unit forms of Dynkin type A. Connected principal unit forms of such type are also classified.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:58:14 +0000</pubDate>
      <link>https://fi.episciences.org/8887</link>
      <guid>https://fi.episciences.org/8887</guid>
      <author>Gonzalez, Jesus Arturo Jimenez</author>
      <dc:creator>Gonzalez, Jesus Arturo Jimenez</dc:creator>
      <content:encoded><![CDATA[In the context of signed line graphs, this article introduces a modified inflation technique to study strong Gram congruence of non-negative (integral quadratic) unit forms, and uses it to show that weak and strong Gram congruence coincide among positive unit forms of Dynkin type A. The concept of inverse of a quiver is also introduced, and is used to obtain and analyze the Coxeter matrix of non-negative unit forms of Dynkin type A. Connected principal unit forms of such type are also classified.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>A Congruence-Based Perspective on Finite Tree Automata</title>
      <description><![CDATA[We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski's style minimization algorithm for tree automata. First, we prove correct this method relying on the following fact: when the automata-based and the language-based congruences coincide, determinizing the automaton yields the minimal one. Such automata-based congruences, in the case of word automata, are defined using pre and post operators. Now we extend these operators to tree automata, a task that is particularly challenging due to the reduced expressive power of deterministic top-down (or equivalently co-deterministic bottom-up) automata. We leverage further our framework to offer an extension of the original result by Brzozowski for word automata.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:57:48 +0000</pubDate>
      <link>https://fi.episciences.org/8885</link>
      <guid>https://fi.episciences.org/8885</guid>
      <author>Ganty, Pierre</author>
      <author>Gutiérrez, Elena</author>
      <author>Valero, Pedro</author>
      <dc:creator>Ganty, Pierre</dc:creator>
      <dc:creator>Gutiérrez, Elena</dc:creator>
      <dc:creator>Valero, Pedro</dc:creator>
      <content:encoded><![CDATA[We provide new insights on the determinization and minimization of tree automata using congruences on trees. From this perspective, we study a Brzozowski's style minimization algorithm for tree automata. First, we prove correct this method relying on the following fact: when the automata-based and the language-based congruences coincide, determinizing the automaton yields the minimal one. Such automata-based congruences, in the case of word automata, are defined using pre and post operators. Now we extend these operators to tree automata, a task that is particularly challenging due to the reduced expressive power of deterministic top-down (or equivalently co-deterministic bottom-up) automata. We leverage further our framework to offer an extension of the original result by Brzozowski for word automata.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Symbolic and Structural Model-Checking</title>
      <description><![CDATA[Brute-force model-checking consists in exhaustive exploration of the state-space of a Petri net, and meets the dreaded state-space explosion problem. In contrast, this paper shows how to solve model-checking problems using a combination of techniques that stay in complexity proportional to the size of the net structure rather than to the state-space size. We combine an SMT based over-approximation to prove that some behaviors are unfeasible, an under-approximation using memory-less sampling of runs to find witness traces or counter-examples, and a set of structural reduction rules that can simplify both the system and the property. This approach was able to win by a clear margin the model-checking contest 2020 for reachability queries as well as deadlock detection, thus demonstrating the practical effectiveness and general applicability of the system of rules presented in this paper.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:51:08 +0000</pubDate>
      <link>https://fi.episciences.org/8888</link>
      <guid>https://fi.episciences.org/8888</guid>
      <author>Thierry-Mieg, Yann</author>
      <dc:creator>Thierry-Mieg, Yann</dc:creator>
      <content:encoded><![CDATA[Brute-force model-checking consists in exhaustive exploration of the state-space of a Petri net, and meets the dreaded state-space explosion problem. In contrast, this paper shows how to solve model-checking problems using a combination of techniques that stay in complexity proportional to the size of the net structure rather than to the state-space size. We combine an SMT based over-approximation to prove that some behaviors are unfeasible, an under-approximation using memory-less sampling of runs to find witness traces or counter-examples, and a set of structural reduction rules that can simplify both the system and the property. This approach was able to win by a clear margin the model-checking contest 2020 for reachability queries as well as deadlock detection, thus demonstrating the practical effectiveness and general applicability of the system of rules presented in this paper.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Automated Repair of Process Models with Non-Local Constraints Using State-Based Region Theory</title>
      <description><![CDATA[State-of-the-art process discovery methods construct free-choice process models from event logs. Consequently, the constructed models do not take into account indirect dependencies between events. Whenever the input behaviour is not free-choice, these methods fail to provide a precise model. In this paper, we propose a novel approach for enhancing free-choice process models by adding non-free-choice constructs discovered a-posteriori via region-based techniques. This allows us to benefit from the performance of existing process discovery methods and the accuracy of the employed fundamental synthesis techniques. We prove that the proposed approach preserves fitness with respect to the event log while improving the precision when indirect dependencies exist. The approach has been implemented and tested on both synthetic and real-life datasets. The results show its effectiveness in repairing models discovered from event logs.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:50:46 +0000</pubDate>
      <link>https://fi.episciences.org/8834</link>
      <guid>https://fi.episciences.org/8834</guid>
      <author>Kalenkova, Anna</author>
      <author>Carmona, Josep</author>
      <author>Polyvyanyy, Artem</author>
      <author>La Rosa, Marcello</author>
      <dc:creator>Kalenkova, Anna</dc:creator>
      <dc:creator>Carmona, Josep</dc:creator>
      <dc:creator>Polyvyanyy, Artem</dc:creator>
      <dc:creator>La Rosa, Marcello</dc:creator>
      <content:encoded><![CDATA[State-of-the-art process discovery methods construct free-choice process models from event logs. Consequently, the constructed models do not take into account indirect dependencies between events. Whenever the input behaviour is not free-choice, these methods fail to provide a precise model. In this paper, we propose a novel approach for enhancing free-choice process models by adding non-free-choice constructs discovered a-posteriori via region-based techniques. This allows us to benefit from the performance of existing process discovery methods and the accuracy of the employed fundamental synthesis techniques. We prove that the proposed approach preserves fitness with respect to the event log while improving the precision when indirect dependencies exist. The approach has been implemented and tested on both synthetic and real-life datasets. The results show its effectiveness in repairing models discovered from event logs.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>On the expressive power of non-deterministic and unambiguous Petri nets over infinite words</title>
      <description><![CDATA[We prove that $\omega$-languages of (non-deterministic) Petri nets and $\omega$-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of $\omega$-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of $\omega$-languages of (non-deterministic) Turing machines. We also show that it is highly undecidable to determine the topological complexity of a Petri net $\omega$-language. Moreover, we infer from the proofs of the above results that the equivalence and the inclusion problems for $\omega$-languages of Petri nets are $\Pi_2^1$-complete, hence also highly undecidable. Additionally, we show that the situation is quite the opposite when considering unambiguous Petri nets, which have the semantic property that at most one accepting run exists on every input. We provide a procedure of determinising them into deterministic Muller counter machines with counter copying. As a consequence, we entail that the $\omega$-languages recognisable by unambiguous Petri nets are $\Delta^0_3$ sets.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:50:26 +0000</pubDate>
      <link>https://fi.episciences.org/8866</link>
      <guid>https://fi.episciences.org/8866</guid>
      <author>Finkel, Olivier</author>
      <author>Skrzypczak, Michał</author>
      <dc:creator>Finkel, Olivier</dc:creator>
      <dc:creator>Skrzypczak, Michał</dc:creator>
      <content:encoded><![CDATA[We prove that $\omega$-languages of (non-deterministic) Petri nets and $\omega$-languages of (non-deterministic) Turing machines have the same topological complexity: the Borel and Wadge hierarchies of the class of $\omega$-languages of (non-deterministic) Petri nets are equal to the Borel and Wadge hierarchies of the class of $\omega$-languages of (non-deterministic) Turing machines. We also show that it is highly undecidable to determine the topological complexity of a Petri net $\omega$-language. Moreover, we infer from the proofs of the above results that the equivalence and the inclusion problems for $\omega$-languages of Petri nets are $\Pi_2^1$-complete, hence also highly undecidable. Additionally, we show that the situation is quite the opposite when considering unambiguous Petri nets, which have the semantic property that at most one accepting run exists on every input. We provide a procedure of determinising them into deterministic Muller counter machines with counter copying. As a consequence, we entail that the $\omega$-languages recognisable by unambiguous Petri nets are $\Delta^0_3$ sets.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Inferring Unobserved Events in Systems With Shared Resources and Queues</title>
      <description><![CDATA[To identify the causes of performance problems or to predict process behavior, it is essential to have correct and complete event data. This is particularly important for distributed systems with shared resources, e.g., one case can block another case competing for the same machine, leading to inter-case dependencies in performance. However, due to a variety of reasons, real-life systems often record only a subset of all events taking place. To understand and analyze the behavior and performance of processes with shared resources, we aim to reconstruct bounds for timestamps of events in a case that must have happened but were not recorded by inference over events in other cases in the system. We formulate and solve the problem by systematically introducing multi-entity concepts in event logs and process models. We introduce a partial-order based model of a multi-entity event log and a corresponding compositional model for multi-entity processes. We define PQR-systems as a special class of multi-entity processes with shared resources and queues. We then study the problem of inferring from an incomplete event log unobserved events and their timestamps that are globally consistent with a PQR-system. We solve the problem by reconstructing unobserved traces of resources and queues according to the PQR-model and derive bounds for their timestamps using a linear program. While the problem is illustrated for material handling systems like baggage handling systems in airports, the approach can be applied to other settings where recording is incomplete. The ideas have been implemented in ProM and were evaluated using both synthetic and real-life event logs.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:50:09 +0000</pubDate>
      <link>https://fi.episciences.org/8824</link>
      <guid>https://fi.episciences.org/8824</guid>
      <author>Fahland, Dirk</author>
      <author>Denisov, Vadim</author>
      <author>van der Aalst, Wil. M. P.</author>
      <dc:creator>Fahland, Dirk</dc:creator>
      <dc:creator>Denisov, Vadim</dc:creator>
      <dc:creator>van der Aalst, Wil. M. P.</dc:creator>
      <content:encoded><![CDATA[To identify the causes of performance problems or to predict process behavior, it is essential to have correct and complete event data. This is particularly important for distributed systems with shared resources, e.g., one case can block another case competing for the same machine, leading to inter-case dependencies in performance. However, due to a variety of reasons, real-life systems often record only a subset of all events taking place. To understand and analyze the behavior and performance of processes with shared resources, we aim to reconstruct bounds for timestamps of events in a case that must have happened but were not recorded by inference over events in other cases in the system. We formulate and solve the problem by systematically introducing multi-entity concepts in event logs and process models. We introduce a partial-order based model of a multi-entity event log and a corresponding compositional model for multi-entity processes. We define PQR-systems as a special class of multi-entity processes with shared resources and queues. We then study the problem of inferring from an incomplete event log unobserved events and their timestamps that are globally consistent with a PQR-system. We solve the problem by reconstructing unobserved traces of resources and queues according to the PQR-model and derive bounds for their timestamps using a linear program. While the problem is illustrated for material handling systems like baggage handling systems in airports, the approach can be applied to other settings where recording is incomplete. The ideas have been implemented in ProM and were evaluated using both synthetic and real-life event logs.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Piecewise Affine Dynamical Models of Timed Petri Nets -- Application to Emergency Call Centers</title>
      <description><![CDATA[We study timed Petri nets, with preselection and priority routing. We represent the behavior of these systems by piecewise affine dynamical systems. We use tools from the theory of nonexpansive mappings to analyze these systems. We establishan equivalence theorem between priority-free fluid timed Petri nets and semi-Markov decision processes, from which we derive the convergence to a periodic regime and the polynomial-time computability of the throughput. More generally, we develop an approach inspired by tropical geometry, characterizing the congestion phases as the cells of a polyhedral complex. We illustrate these results by a current application to the performance evaluation of emergency call centers in the Paris area. We show that priorities can lead to a paradoxical behavior: in certain regimes, the throughput of the most prioritary task may not be an increasing function of the resources.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:41:55 +0000</pubDate>
      <link>https://fi.episciences.org/8822</link>
      <guid>https://fi.episciences.org/8822</guid>
      <author>Allamigeon, Xavier</author>
      <author>Boyet, Marin</author>
      <author>Gaubert, Stéphane</author>
      <dc:creator>Allamigeon, Xavier</dc:creator>
      <dc:creator>Boyet, Marin</dc:creator>
      <dc:creator>Gaubert, Stéphane</dc:creator>
      <content:encoded><![CDATA[We study timed Petri nets, with preselection and priority routing. We represent the behavior of these systems by piecewise affine dynamical systems. We use tools from the theory of nonexpansive mappings to analyze these systems. We establishan equivalence theorem between priority-free fluid timed Petri nets and semi-Markov decision processes, from which we derive the convergence to a periodic regime and the polynomial-time computability of the throughput. More generally, we develop an approach inspired by tropical geometry, characterizing the congestion phases as the cells of a polyhedral complex. We illustrate these results by a current application to the performance evaluation of emergency call centers in the Paris area. We show that priorities can lead to a paradoxical behavior: in certain regimes, the throughput of the most prioritary task may not be an increasing function of the resources.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>The Complexity of Synthesis of $b$-Bounded Petri Nets</title>
      <description><![CDATA[For a fixed type of Petri nets $\tau$, \textsc{$\tau$-Synthesis} is the task of finding for a given transition system $A$ a Petri net $N$ of type $\tau$ ($\tau$-net, for short) whose reachability graph is isomorphic to $A$ if there is one. The decision version of this search problem is called \textsc{$\tau$-Solvability}. If an input $A$ allows a positive decision, then it is called $\tau$-solvable and a sought net $N$ $\tau$-solves $A$. As a well known fact, $A$ is $\tau$-solvable if and only if it has the so-called $\tau$-\emph{event state separation property} ($\tau$-ESSP, for short) and the $\tau$-\emph{state separation property} ($\tau$-SSP, for short). The question whether $A$ has the $\tau$-ESSP or the $\tau$-SSP defines also decision problems. In this paper, for all $b\in \mathbb{N}$, we completely characterize the computational complexity of \textsc{$\tau$-Solvability}, \textsc{$\tau$-ESSP} and \textsc{$\tau$-SSP} for the types of pure $b$-bounded Place/Transition-nets, the $b$-bounded Place/Transition-nets and their corresponding $\mathbb{Z}_{b+1}$-extensions.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:40:31 +0000</pubDate>
      <link>https://fi.episciences.org/8821</link>
      <guid>https://fi.episciences.org/8821</guid>
      <author>Tredup, Ronny</author>
      <dc:creator>Tredup, Ronny</dc:creator>
      <content:encoded><![CDATA[For a fixed type of Petri nets $\tau$, \textsc{$\tau$-Synthesis} is the task of finding for a given transition system $A$ a Petri net $N$ of type $\tau$ ($\tau$-net, for short) whose reachability graph is isomorphic to $A$ if there is one. The decision version of this search problem is called \textsc{$\tau$-Solvability}. If an input $A$ allows a positive decision, then it is called $\tau$-solvable and a sought net $N$ $\tau$-solves $A$. As a well known fact, $A$ is $\tau$-solvable if and only if it has the so-called $\tau$-\emph{event state separation property} ($\tau$-ESSP, for short) and the $\tau$-\emph{state separation property} ($\tau$-SSP, for short). The question whether $A$ has the $\tau$-ESSP or the $\tau$-SSP defines also decision problems. In this paper, for all $b\in \mathbb{N}$, we completely characterize the computational complexity of \textsc{$\tau$-Solvability}, \textsc{$\tau$-ESSP} and \textsc{$\tau$-SSP} for the types of pure $b$-bounded Place/Transition-nets, the $b$-bounded Place/Transition-nets and their corresponding $\mathbb{Z}_{b+1}$-extensions.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Cost Problems for Parametric Time Petri Nets</title>
      <description><![CDATA[We investigate the problem of parameter synthesis for time Petri nets with a cost variable that evolves both continuously with time, and discretely when firing transitions. More precisely, parameters are rational symbolic constants used for time constraints on the firing of transitions and we want to synthesise all their values such that some marking is reachable, with a cost that is either minimal or simply less than a given bound. We first prove that the mere existence of values for the parameters such that the latter property holds is undecidable. We nonetheless provide symbolic semi-algorithms for the two synthesis problems and we prove them both sound and complete when they terminate. We also show how to modify them for the case when parameter values are integers. Finally, we prove that these modified versions terminate if parameters are bounded. While this is to be expected since there are now only a finite number of possible parameter values, our algorithms are symbolic and thus avoid an explicit enumeration of all those values. Furthermore, the results are symbolic constraints representing finite unions of convex polyhedra that are easily amenable to further analysis through linear programming. We finally report on the implementation of the approach in Romeo, a software tool for the analysis of time Petri nets.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:39:02 +0000</pubDate>
      <link>https://fi.episciences.org/8848</link>
      <guid>https://fi.episciences.org/8848</guid>
      <author>Lime, Didier</author>
      <author>Roux, Olivier H.</author>
      <author>Seidner, Charlotte</author>
      <dc:creator>Lime, Didier</dc:creator>
      <dc:creator>Roux, Olivier H.</dc:creator>
      <dc:creator>Seidner, Charlotte</dc:creator>
      <content:encoded><![CDATA[We investigate the problem of parameter synthesis for time Petri nets with a cost variable that evolves both continuously with time, and discretely when firing transitions. More precisely, parameters are rational symbolic constants used for time constraints on the firing of transitions and we want to synthesise all their values such that some marking is reachable, with a cost that is either minimal or simply less than a given bound. We first prove that the mere existence of values for the parameters such that the latter property holds is undecidable. We nonetheless provide symbolic semi-algorithms for the two synthesis problems and we prove them both sound and complete when they terminate. We also show how to modify them for the case when parameter values are integers. Finally, we prove that these modified versions terminate if parameters are bounded. While this is to be expected since there are now only a finite number of possible parameter values, our algorithms are symbolic and thus avoid an explicit enumeration of all those values. Furthermore, the results are symbolic constraints representing finite unions of convex polyhedra that are easily amenable to further analysis through linear programming. We finally report on the implementation of the approach in Romeo, a software tool for the analysis of time Petri nets.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Investigating Reversibility of Steps in Petri Nets</title>
      <description><![CDATA[In reversible computations one is interested in the development of mechanisms allowing to undo the effects of executed actions. The past research has been concerned mainly with reversing single actions. In this paper, we consider the problem of reversing the effect of the execution of groups of actions (steps). Using Petri nets as a system model, we introduce concepts related to this new scenario, generalising notions used in the single action case. We then present properties arising when reverse actions are allowed in place/transition nets (pt-nets). We obtain both positive and negative results, showing that allowing steps makes reversibility more problematic than in the interleaving/sequential case. In particular, we demonstrate that there is a crucial difference between reversing steps which are sets and those which are true multisets. Moreover, in contrast to sequential semantics, splitting reverses does not lead to a general method for reversing bounded pt-nets. We then show that a suitable solution can be obtained by combining split reverses with weighted read arcs.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:35:12 +0000</pubDate>
      <link>https://fi.episciences.org/8840</link>
      <guid>https://fi.episciences.org/8840</guid>
      <author>Escrig, David de Frutos</author>
      <author>Koutny, Maciej</author>
      <author>Mikulski, Łukasz</author>
      <dc:creator>Escrig, David de Frutos</dc:creator>
      <dc:creator>Koutny, Maciej</dc:creator>
      <dc:creator>Mikulski, Łukasz</dc:creator>
      <content:encoded><![CDATA[In reversible computations one is interested in the development of mechanisms allowing to undo the effects of executed actions. The past research has been concerned mainly with reversing single actions. In this paper, we consider the problem of reversing the effect of the execution of groups of actions (steps). Using Petri nets as a system model, we introduce concepts related to this new scenario, generalising notions used in the single action case. We then present properties arising when reverse actions are allowed in place/transition nets (pt-nets). We obtain both positive and negative results, showing that allowing steps makes reversibility more problematic than in the interleaving/sequential case. In particular, we demonstrate that there is a crucial difference between reversing steps which are sets and those which are true multisets. Moreover, in contrast to sequential semantics, splitting reverses does not lead to a general method for reversing bounded pt-nets. We then show that a suitable solution can be obtained by combining split reverses with weighted read arcs.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Coverability, Termination, and Finiteness in Recursive Petri Nets</title>
      <description><![CDATA[In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and context-free grammars, most of the usual problems (reachability, coverability, finiteness, boundedness and termination) were known to be solvable by using non-primitive recursive algorithms. For almost all other extended Petri nets models containing a stack, the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability, termination, boundedness and finiteness problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get a more powerful model than Petri net for free.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:34:42 +0000</pubDate>
      <link>https://fi.episciences.org/8876</link>
      <guid>https://fi.episciences.org/8876</guid>
      <author>Finkel, Alain</author>
      <author>Haddad, Serge</author>
      <author>Khmelnitsky, Igor</author>
      <dc:creator>Finkel, Alain</dc:creator>
      <dc:creator>Haddad, Serge</dc:creator>
      <dc:creator>Khmelnitsky, Igor</dc:creator>
      <content:encoded><![CDATA[In the early two-thousands, Recursive Petri nets have been introduced in order to model distributed planning of multi-agent systems for which counters and recursivity were necessary. Although Recursive Petri nets strictly extend Petri nets and context-free grammars, most of the usual problems (reachability, coverability, finiteness, boundedness and termination) were known to be solvable by using non-primitive recursive algorithms. For almost all other extended Petri nets models containing a stack, the complexity of coverability and termination are unknown or strictly larger than EXPSPACE. In contrast, we establish here that for Recursive Petri nets, the coverability, termination, boundedness and finiteness problems are EXPSPACE-complete as for Petri nets. From an expressiveness point of view, we show that coverability languages of Recursive Petri nets strictly include the union of coverability languages of Petri nets and context-free languages. Thus we get a more powerful model than Petri net for free.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Articulations and Products of Transition Systems and their Applications to Petri Net Synthesis</title>
      <description><![CDATA[In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the original system. Then corresponding Petri Net composition operators are searched to combine the solutions of the various components into a solution of the original system. The paper presents two such techniques, which may be combined: products and articulations. They may also be used to structure transition systems, and to analyse the performance of synthesis techniques when applied to such structures.]]></description>
      <pubDate>Thu, 23 Dec 2021 13:33:43 +0000</pubDate>
      <link>https://fi.episciences.org/8859</link>
      <guid>https://fi.episciences.org/8859</guid>
      <author>Devillers, Raymond</author>
      <dc:creator>Devillers, Raymond</dc:creator>
      <content:encoded><![CDATA[In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the original system. Then corresponding Petri Net composition operators are searched to combine the solutions of the various components into a solution of the original system. The paper presents two such techniques, which may be combined: products and articulations. They may also be used to structure transition systems, and to analyse the performance of synthesis techniques when applied to such structures.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Perpetual Free-choice Petri nets are lucent -- proof of a theorem of van der Aalst using CP-exhaustions</title>
      <description><![CDATA[Van der Aalst's theorem is an important result for the analysis and synthesis of process models. The paper proves the theorem by exhausting perpetual free-choice Petri nets by CP-subnets. The resulting T-systems are investigated by elementary methods.]]></description>
      <pubDate>Thu, 18 Nov 2021 10:20:49 +0000</pubDate>
      <link>https://fi.episciences.org/8698</link>
      <guid>https://fi.episciences.org/8698</guid>
      <author>Wehler, Joachim</author>
      <dc:creator>Wehler, Joachim</dc:creator>
      <content:encoded><![CDATA[Van der Aalst's theorem is an important result for the analysis and synthesis of process models. The paper proves the theorem by exhausting perpetual free-choice Petri nets by CP-subnets. The resulting T-systems are investigated by elementary methods.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>The inverse of Ackermann function is computable in linear time</title>
      <description><![CDATA[We propose a detailed proof of the fact that the inverse of Ackermann function is computable in linear time.]]></description>
      <pubDate>Thu, 18 Nov 2021 10:20:13 +0000</pubDate>
      <link>https://fi.episciences.org/8694</link>
      <guid>https://fi.episciences.org/8694</guid>
      <author>Sureson, Claude</author>
      <dc:creator>Sureson, Claude</dc:creator>
      <content:encoded><![CDATA[We propose a detailed proof of the fact that the inverse of Ackermann function is computable in linear time.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Testing Boolean Functions Properties</title>
      <description><![CDATA[The goal in the area of functions property testing is to determine whether a given black-box Boolean function has a particular given property or is $\varepsilon$-far from having that property. We investigate here several types of properties testing for Boolean functions (identity, correlations and balancedness) using the Deutsch-Jozsa algorithm (for the Deutsch-Jozsa (D-J) problem) and also the amplitude amplification technique. At first, we study here a particular testing problem: namely whether a given Boolean function $f$, of $n$ variables, is identical with a given function $g$ or is $\varepsilon$-far from $g$, where $\varepsilon$ is the parameter. We present a one-sided error quantum algorithm to deal with this problem that has the query complexity $O(\frac{1}{\sqrt{\varepsilon}})$. Moreover, we show that our quantum algorithm is optimal. Afterwards we show that the classical randomized query complexity of this problem is $\Theta(\frac{1}{\varepsilon})$. Secondly, we consider the D-J problem from the perspective of functional correlations and let $C(f,g)$ denote the correlation of $f$ and $g$. We propose an exact quantum algorithm for making distinction between $|C(f,g)|=\varepsilon$ and $|C(f,g)|=1$ using six queries, while the classical deterministic query complexity for this problem is $\Theta(2^{n})$ queries. Finally, we propose a one-sided error quantum query algorithm for testing whether one Boolean function is balanced versus $\varepsilon$-far balanced using $O(\frac{1}{\varepsilon})$ queries. We also prove here that our quantum algorithm for balancedness testing is optimal. At the same time, for this balancedness testing problem we present a classical randomized algorithm with query complexity of $O(1/\varepsilon^{2})$. Also this randomized algorithm is optimal. Besides, we link the problems considered here together and generalize them to the general case.]]></description>
      <pubDate>Thu, 18 Nov 2021 10:19:47 +0000</pubDate>
      <link>https://fi.episciences.org/8697</link>
      <guid>https://fi.episciences.org/8697</guid>
      <author>Xie, Zhengwei</author>
      <author>Qiu, Daowen</author>
      <author>Cai, Guangya</author>
      <author>Gruska, Jozef</author>
      <author>Mateus, Paulo</author>
      <dc:creator>Xie, Zhengwei</dc:creator>
      <dc:creator>Qiu, Daowen</dc:creator>
      <dc:creator>Cai, Guangya</dc:creator>
      <dc:creator>Gruska, Jozef</dc:creator>
      <dc:creator>Mateus, Paulo</dc:creator>
      <content:encoded><![CDATA[The goal in the area of functions property testing is to determine whether a given black-box Boolean function has a particular given property or is $\varepsilon$-far from having that property. We investigate here several types of properties testing for Boolean functions (identity, correlations and balancedness) using the Deutsch-Jozsa algorithm (for the Deutsch-Jozsa (D-J) problem) and also the amplitude amplification technique. At first, we study here a particular testing problem: namely whether a given Boolean function $f$, of $n$ variables, is identical with a given function $g$ or is $\varepsilon$-far from $g$, where $\varepsilon$ is the parameter. We present a one-sided error quantum algorithm to deal with this problem that has the query complexity $O(\frac{1}{\sqrt{\varepsilon}})$. Moreover, we show that our quantum algorithm is optimal. Afterwards we show that the classical randomized query complexity of this problem is $\Theta(\frac{1}{\varepsilon})$. Secondly, we consider the D-J problem from the perspective of functional correlations and let $C(f,g)$ denote the correlation of $f$ and $g$. We propose an exact quantum algorithm for making distinction between $|C(f,g)|=\varepsilon$ and $|C(f,g)|=1$ using six queries, while the classical deterministic query complexity for this problem is $\Theta(2^{n})$ queries. Finally, we propose a one-sided error quantum query algorithm for testing whether one Boolean function is balanced versus $\varepsilon$-far balanced using $O(\frac{1}{\varepsilon})$ queries. We also prove here that our quantum algorithm for balancedness testing is optimal. At the same time, for this balancedness testing problem we present a classical randomized algorithm with query complexity of $O(1/\varepsilon^{2})$. Also this randomized algorithm is optimal. Besides, we link the problems considered here together and generalize them to the general case.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Query-points visibility constraint minimum link paths in simple polygons</title>
      <description><![CDATA[We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning $P$ into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points $s$, $t$ and a query point $q$. Then, the proposed solution is extended to a general case for three arbitrary query points $s$, $t$ and $q$. In the former, we propose an algorithm with $O(n)$ preprocessing time. Extending this approach for the latter case, we develop an algorithm with $O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between $s$, $t$ as well as the path are provided in time $O(\log n)$ and $O(m+\log n)$, respectively, for the above two cases, where $m$ is the number of links.]]></description>
      <pubDate>Thu, 18 Nov 2021 10:14:43 +0000</pubDate>
      <link>https://fi.episciences.org/8626</link>
      <guid>https://fi.episciences.org/8626</guid>
      <author>Zarrabi, Mohammad Reza</author>
      <author>Charkari, Nasrollah Moghaddam</author>
      <dc:creator>Zarrabi, Mohammad Reza</dc:creator>
      <dc:creator>Charkari, Nasrollah Moghaddam</dc:creator>
      <content:encoded><![CDATA[We study the query version of constrained minimum link paths between two points inside a simple polygon $P$ with $n$ vertices such that there is at least one point on the path, visible from a query point. The method is based on partitioning $P$ into a number of faces of equal link distance from a point, called a link-based shortest path map (SPM). Initially, we solve this problem for two given points $s$, $t$ and a query point $q$. Then, the proposed solution is extended to a general case for three arbitrary query points $s$, $t$ and $q$. In the former, we propose an algorithm with $O(n)$ preprocessing time. Extending this approach for the latter case, we develop an algorithm with $O(n^3)$ preprocessing time. The link distance of a $q$-$visible$ path between $s$, $t$ as well as the path are provided in time $O(\log n)$ and $O(m+\log n)$, respectively, for the above two cases, where $m$ is the number of links.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Edge Forcing in Butterfly Networks</title>
      <description><![CDATA[A zero forcing set is a set $S$ of vertices of a graph $G$, called forced vertices of $G$, which are able to force the entire graph by applying the following process iteratively: At any particular instance of time, if any forced vertex has a unique unforced neighbor, it forces that neighbor. In this paper, we introduce a variant of zero forcing set that induces independent edges and name it as edge-forcing set. The minimum cardinality of an edge-forcing set is called the edge-forcing number. We prove that the edge-forcing problem of determining the edge-forcing number is NP-complete. Further, we study the edge-forcing number of butterfly networks. We obtain a lower bound on the edge-forcing number of butterfly networks and prove that this bound is tight for butterfly networks of dimensions 2, 3, 4 and 5 and obtain an upper bound for the higher dimensions.]]></description>
      <pubDate>Thu, 18 Nov 2021 10:14:26 +0000</pubDate>
      <link>https://fi.episciences.org/8644</link>
      <guid>https://fi.episciences.org/8644</guid>
      <author>G., Jessy Sujana</author>
      <author>Rajalaxmi, T. M.</author>
      <author>Rajasingh, Indra</author>
      <author>Rajan, R. Sundara</author>
      <dc:creator>G., Jessy Sujana</dc:creator>
      <dc:creator>Rajalaxmi, T. M.</dc:creator>
      <dc:creator>Rajasingh, Indra</dc:creator>
      <dc:creator>Rajan, R. Sundara</dc:creator>
      <content:encoded><![CDATA[A zero forcing set is a set $S$ of vertices of a graph $G$, called forced vertices of $G$, which are able to force the entire graph by applying the following process iteratively: At any particular instance of time, if any forced vertex has a unique unforced neighbor, it forces that neighbor. In this paper, we introduce a variant of zero forcing set that induces independent edges and name it as edge-forcing set. The minimum cardinality of an edge-forcing set is called the edge-forcing number. We prove that the edge-forcing problem of determining the edge-forcing number is NP-complete. Further, we study the edge-forcing number of butterfly networks. We obtain a lower bound on the edge-forcing number of butterfly networks and prove that this bound is tight for butterfly networks of dimensions 2, 3, 4 and 5 and obtain an upper bound for the higher dimensions.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Efficient algorithms for maximum induced matching problem in permutation and trapezoid graphs</title>
      <description><![CDATA[We first design an $\mathcal{O}(n^2)$ solution for finding a maximum induced matching in permutation graphs given their permutation models, based on a dynamic programming algorithm with the aid of the sweep line technique. With the support of the disjoint-set data structure, we improve the complexity to $\mathcal{O}(m + n)$. Consequently, we extend this result to give an $\mathcal{O}(m + n)$ algorithm for the same problem in trapezoid graphs. By combining our algorithms with the current best graph identification algorithms, we can solve the MIM problem in permutation and trapezoid graphs in linear and $\mathcal{O}(n^2)$ time, respectively. Our results are far better than the best known $\mathcal{O}(mn)$ algorithm for the maximum induced matching problem in both graph classes, which was proposed by Habib et al.]]></description>
      <pubDate>Thu, 18 Nov 2021 10:14:08 +0000</pubDate>
      <link>https://fi.episciences.org/8685</link>
      <guid>https://fi.episciences.org/8685</guid>
      <author>Nguyen, Viet Dung</author>
      <author>Pham, Ba Thai</author>
      <author>Do, Phan Thuan</author>
      <dc:creator>Nguyen, Viet Dung</dc:creator>
      <dc:creator>Pham, Ba Thai</dc:creator>
      <dc:creator>Do, Phan Thuan</dc:creator>
      <content:encoded><![CDATA[We first design an $\mathcal{O}(n^2)$ solution for finding a maximum induced matching in permutation graphs given their permutation models, based on a dynamic programming algorithm with the aid of the sweep line technique. With the support of the disjoint-set data structure, we improve the complexity to $\mathcal{O}(m + n)$. Consequently, we extend this result to give an $\mathcal{O}(m + n)$ algorithm for the same problem in trapezoid graphs. By combining our algorithms with the current best graph identification algorithms, we can solve the MIM problem in permutation and trapezoid graphs in linear and $\mathcal{O}(n^2)$ time, respectively. Our results are far better than the best known $\mathcal{O}(mn)$ algorithm for the maximum induced matching problem in both graph classes, which was proposed by Habib et al.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Time-free solution to independent set problem using P systems with active membranes</title>
      <description><![CDATA[Membrane computing is a branch of natural computingwhich abstracts fromthe structure and the functioning of living cells. The computation models obtained in the field of membrane computing are usually called P systems. P systems have been used to solve computationally hard problems efficiently on the assumption that the execution of each rule is completed in exactly one time-unit (a global clock is assumed for timing and synchronizing the execution of rules). However, in biological reality, different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, with this biological reality, we give a time-free solution to independent set problemusing P systems with active membranes, which solve the problem independent of the execution time of the involved rules.]]></description>
      <pubDate>Thu, 18 Nov 2021 10:13:46 +0000</pubDate>
      <link>https://fi.episciences.org/8636</link>
      <guid>https://fi.episciences.org/8636</guid>
      <author>Jin, Yu</author>
      <author>Song, Bosheng</author>
      <author>Li, Yanyan</author>
      <author>Zhu, Ying</author>
      <dc:creator>Jin, Yu</dc:creator>
      <dc:creator>Song, Bosheng</dc:creator>
      <dc:creator>Li, Yanyan</dc:creator>
      <dc:creator>Zhu, Ying</dc:creator>
      <content:encoded><![CDATA[Membrane computing is a branch of natural computingwhich abstracts fromthe structure and the functioning of living cells. The computation models obtained in the field of membrane computing are usually called P systems. P systems have been used to solve computationally hard problems efficiently on the assumption that the execution of each rule is completed in exactly one time-unit (a global clock is assumed for timing and synchronizing the execution of rules). However, in biological reality, different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, with this biological reality, we give a time-free solution to independent set problemusing P systems with active membranes, which solve the problem independent of the execution time of the involved rules.]]></content:encoded>
      <slash:comments>0</slash:comments>
    </item>
    <item>
      <title>Exact and Approximate Algorithms for Computing Betweenness Centrality in Directed Graphs</title>
      <description><![CDATA[Graphs (networks) are an important tool to model data in different domains. Real-world graphs are usually directed, where the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network $G$ and a vertex $r \in V(G)$, we propose an exact algorithm to compute betweenness score of $r$. Our algorithm pre-computes a set $\mathcal{RV}(r)$, which is used to prune a huge amount of computations that do not contribute to the betweenness score of $r$. Time complexity of our algorithm depends on $|\mathcal{RV}(r)|$ and it is respectively $\Theta(|\mathcal{RV}(r)|\cdot|E(G)|)$ and $\Theta(|\mathcal{RV}(r)|\cdot|E(G)|+|\mathcal{RV}(r)|\cdot|V(G)|\log |V(G)|)$ for unweighted graphs and weighted graphs with positive weights. $|\mathcal{RV}(r)|$ is bounded from above by $|V(G)|-1$ and in most cases, it is a small constant. Then, for the cases where $\mathcal{RV}(r)$ is large, we present a simple randomized algorithm that samples from $\mathcal{RV}(r)$ and performs computations for only the sampled elements. We show that this algorithm provides an $(\epsilon,\delta)$-approximation to the betweenness score of $r$. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that for estimating betweenness score of a single vertex, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also reveal that our algorithm improves the existing algorithms when someone is interested in computing betweenness values of the vertices in a set whose cardinality is very small.]]></description>
      <pubDate>Thu, 18 Nov 2021 08:31:34 +0000</pubDate>
      <link>https://fi.episciences.org/8624</link>
      <guid>https://fi.episciences.org/8624</guid>
      <author>Chehreghani, Mostafa Haghir</author>
      <author>Bifet, Albert</author>
      <author>Abdessalem, Talel</author>
      <dc:creator>Chehreghani, Mostafa Haghir</dc:creator>
      <dc:creator>Bifet, Albert</dc:creator>
      <dc:creator>Abdessalem, Talel</dc:creator>
      <content:encoded><![CDATA[Graphs (networks) are an important tool to model data in different domains. Real-world graphs are usually directed, where the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network $G$ and a vertex $r \in V(G)$, we propose an exact algorithm to compute betweenness score of $r$. Our algorithm pre-computes a set $\mathcal{RV}(r)$, which is used to prune a huge amount of computations that do not contribute to the betweenness score of $r$. Time complexity of our algorithm depends on $|\mathcal{RV}(r)|$ and it is respectively $\Theta(|\mathcal{RV}(r)|\cdot|E(G)|)$ and $\Theta(|\mathcal{RV}(r)|\cdot|E(G)|+|\mathcal{RV}(r)|\cdot|V(G)|\log |V(G)|)$ for unweighted graphs and weighted graphs with positive weights. $|\mathcal{RV}(r)|$ is bounded from above by $|V(G)|-1$ and in most cases, it is a small constant. Then, for the cases where $\mathcal{RV}(r)$ is large, we present a simple randomized algorithm that samples from $\mathcal{RV}(r)$ and performs computations for only the sampled elements. We show that this algorithm provides an $(\epsilon,\delta)$-approximation to the betweenness score of $r$. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that for estimating betweenness score of a single vertex, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also reveal that our algorithm improves the existing algorithms when someone is interested in computing betweenness values of the vertices in a set whose cardinality is very small.]]></content:encoded>
      <slash:comments>0</slash:comments>
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