Minimization and Canonization of GFG Transition-Based Automata
| Autor: | Radi, Bader Abu, Kupferman, Orna |
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| Rok vydání: | 2021 |
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| Zdroj: | Logical Methods in Computer Science, Volume 18, Issue 3 (August 2, 2022) lmcs:7587 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.46298/lmcs-18(3:16)2022 |
| Popis: | While many applications of automata in formal methods can use nondeterministic 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 B\"uchi and co-B\"uchi 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-B\"uchi word automata with transition-based acceptance. Thus, a run is accepting if it traverses a set $\alpha$ 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-B\"uchi word automata: all minimal automata have isomorphic safe components (namely components obtained by restricting the transitions to these not in $\alpha$) and once we saturate the automata with $\alpha$-transitions, we get full isomorphism. Comment: arXiv admin note: substantial text overlap with arXiv:2009.10885 |
| Databáze: | arXiv |
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