eng
episciences.org
Fundamenta Informaticae
0169-2968
1875-8681
2022-10-21
Volume 187, Issues 2-4: Petri...
10.46298/fi-2022-8813
8813
journal article
Some Basic Techniques allowing Petri Net Synthesis: Complexity and Algorithmic Issues
Raymond Devillers
Ronny Tredup
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
$c\geq 1$.
https://fi.episciences.org/8813/pdf
Computer Science - Formal Languages and Automata Theory