Christof Löding ; Max Philip Stachon - On Minimization and Learning of Deterministic $\omega$-Automata in the Presence of Don't Care Words

fi:10322 - Fundamenta Informaticae, July 1, 2023, Volume 189, Issue 1
On Minimization and Learning of Deterministic $\omega$-Automata in the Presence of Don't Care WordsArticle

Authors: Christof Löding ; Max Philip Stachon

    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 Büchi 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.


    Volume: Volume 189, Issue 1
    Published on: July 1, 2023
    Accepted on: April 25, 2023
    Submitted on: November 17, 2022
    Keywords: Computer Science - Formal Languages and Automata Theory,F.1.1,F.4.3

    Consultation statistics

    This page has been seen 278 times.
    This article's PDF has been downloaded 153 times.