MINIMIZATION AND CANONIZATION OF GFG TRANSITION-BASED AUTOMATA

Bader Abu Radi, Orna Kupferman

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

While many applications of automata in formal methods can use nonde-terministic automata, some applications, most notably synthesis, need deterministic or good-for-games (GFG) automata. The latter are nondeterministic automata that can resolve their nondeterministic choices in a way that only depends on the past. The minimization problem for deterministic Büchi and co-Büchi word automata is NP-complete. In particular, no canonical minimal deterministic automaton exists, and a language may have different minimal deterministic automata. We describe a polynomial minimization algorithm for GFG co-Büchi word automata with transition-based acceptance. Thus, a run is accepting if it traverses a set α of designated transitions only finitely often. Our algorithm is based on a sequence of transformations we apply to the automaton, on top of which a minimal quotient automaton is defined. We use our minimization algorithm to show canonicity for transition-based GFG co-Büchi word automata: all minimal automata have isomorphic safe components (namely components obtained by restricting the transitions to these not in α) and once we saturate the automata with α-transitions, we get full isomorphism.

Original languageAmerican English
Pages (from-to)16:1-16:33
JournalLogical Methods in Computer Science
Volume18
Issue number3
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022, B. Abu Radi and O. Kupferman.

Keywords

  • Canonization
  • Determinisitc Automata on Infinite Words
  • Good-For-Games Automata
  • Minimization
  • co-Büchi acceptance condition

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