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Specifying timed state sequences in powerful decidable logics and timed automata

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Formal Techniques in Real-Time and Fault-Tolerant Systems (FTRTFT 1994, ProCoS 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 863))

Abstract

A monadic second-order language, denoted by \(\mathcal{L}d\), is introduced for the specification of sets of timed state sequences. A fragment of \(\mathcal{L}d\), denoted by

, is proved to be expressively complete for timed automata (Alur and Dill), i.e., every timed regular language is definable by a

-formula and every

-formula defines a timed regular language. As a consequence the satisfiability problem for

is decidable.

Timed temporal logics are shown to be effectively embeddable into

and hence turn out to have a decidable theory. This applies to TLГ (Manna and Pnueli) and EMITLp, which is obtained by extending the logic MITLp (Alur and Henzinger) by automata operators (Sistla, Vardi, and Wolper).

For every positive natural number k the full monadic second-order logic \(\mathcal{L}d\) and

are equally expressive modulo the set of timed state sequences of variability ≤ k. Therefore the \(\mathcal{L}d\)-theory of the set of timed state sequences of variability ≤ k is decidable.

This paper was written during the author's stay at Laboratoire Bordelais de Recherche en Informatique (LaBRI). The presented results are part of the author's dissertation [24].

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  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-UniversitÄt zu Kiel, D-24098, Kiel, Germany

    Thomas Wilke

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  1. Thomas Wilke
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Hans Langmaack Willem-Paul de Roever Jan Vytopil

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Wilke, T. (1994). Specifying timed state sequences in powerful decidable logics and timed automata. In: Langmaack, H., de Roever, WP., Vytopil, J. (eds) Formal Techniques in Real-Time and Fault-Tolerant Systems. FTRTFT ProCoS 1994 1994. Lecture Notes in Computer Science, vol 863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58468-4_191

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  • DOI: https://doi.org/10.1007/3-540-58468-4_191

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