History-deterministic Timed Automata

Sougata Bose , Thomas A. Henzinger , Karoliina Lehtinen (1) , Sven Schewe , Patrick Totzke

1 MOVE - Modélisation et Vérification

We explore the notion of history-determinism in the context of timed automata (TA) over infinite timed words. History-deterministic (HD) automata are those in which nondeterminism can be resolved on the fly, based on the run constructed thus far. History-determinism is a robust property that admits different game-based characterisations, and HD specifications allow for game-based verification without an expensive determinization step. We show that the class of timed $\omega$-languages recognised by HD timed automata strictly extends that of deterministic ones, and is strictly included in those recognised by fully non-deterministic TA. For non-deterministic timed automata it is known that universality is already undecidable for B\"uchi TA. For history-deterministic TA with arbitrary parity acceptance, we show that timed universality, inclusion, and synthesis all remain decidable and are EXPTIME-complete. For the subclass of TA with safety or reachability acceptance, one can decide (in EXPTIME) whether such an automaton is history-deterministic. If so, it can effectively determinized without introducing new automata states.

Mots clés: History-determinism; Good-for-games; fair simulation; synthesis; Timed Automata

Domaines: Informatique [cs]

Sougata Bose, Thomas A. Henzinger, Karoliina Lehtinen, Sven Schewe, Patrick Totzke. History-deterministic Timed Automata. 2023. ⟨hal-04271355⟩