Explorable Automata

Explorable automata

Emile Hazard (1, 2) , Denis Kuperberg (1, 2, 3)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 PLUME - Preuves et Langages
3 CNRS - Centre National de la Recherche Scientifique

We define the class of explorable automata on finite or infinite words. This is a generalization of History-Deterministic (HD) automata, where this time non-deterministic choices can be resolved by building finitely many simultaneous runs instead of just one. We show that recognizing HD automata among explorable ones is in PTime, thereby giving a strong link between the two notions. We then show that recognizing explorable automata is ExpTime-complete, in the case of finite words or Büchi automata. Additionally, we define the notion of ω-explorable automata on infinite words, where countably many runs can be used to resolve the non-deterministic choices. We show that all reachability automata are ω-explorable, but this is not the case for safety ones. We finally show ExpTime-completeness for ω-explorability of automata on infinite words, covering the safety and co-Büchi acceptance conditions.

Mots clés: Nondeterminism; automata; complexity; Theory of computation → Formal languages and automata theory

Domaines: Théorie et langage formel [cs.FL]

Emile Hazard, Denis Kuperberg. Explorable Automata. CSL 2023, Feb 2023, Warsaw, Poland. pp.24:1--24:18, ⟨10.4230/LIPIcs.CSL.2023.24⟩. ⟨hal-03669659v2⟩