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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Undecidable Problems About Timed Automata
verfasst von : Olivier Finkel
Erschienen in: Formal Modeling and Analysis of Timed Systems
Verlag: Springer Berlin Heidelberg
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We solve some decision problems for timed automata which were raised by S. Tripakis in [Tri04] and by E. Asarin in [Asa04]. 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 Π
1
1
-hard, hence highly undecidable (located beyond the arithmetical hierarchy).