Undecidable Problems About Timed Automata

Abstract : We solve some decision problems for timed automata which were recently raised by S. Tripakis in [ Folk Theorems on the Determinization and Minimization of Timed Automata, in the Proceedings of the International Workshop FORMATS'2003, LNCS, Volume 2791, p. 182-188, 2004 ] and by E. Asarin in [ Challenges in Timed Languages, From Applied Theory to Basic Theory, Bulletin of the EATCS, Volume 83, p. 106-120, 2004 ]. In particular, we show that one cannot decide whether a given timed automaton is determinizable or whether the complement of a timed regular language is timed regular. We show that the problem of the minimization of the number of clocks of a timed automaton is undecidable. It is also undecidable whether the shuffle of two timed regular languages is timed regular. We show that in the case of timed Büchi automata accepting infinite timed words some of these problems are Pi^1_1-hard, hence highly undecidable (located beyond the arithmetical hierarchy).
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https://hal.archives-ouvertes.fr/hal-00121529
Contributeur : Olivier Finkel <>
Soumis le : dimanche 9 décembre 2007 - 21:09:18
Dernière modification le : vendredi 4 janvier 2019 - 17:32:32
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  • HAL Id : hal-00121529, version 2
  • ARXIV : 0712.1363

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Olivier Finkel. Undecidable Problems About Timed Automata. FORMATS'06, 2006, France. pp.187-199. ⟨hal-00121529v2⟩

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