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Timed Automata and the Theory of Real Numbers

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CONCUR’99 Concurrency Theory (CONCUR 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1664))

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Abstract

A configuration of a timed automaton is given by a control state and finitely many clock (real) values. We show here that the binary reachability relation between configurations of a timed automaton is definable in an additive theory of real numbers, which is decidable. This result implies the decidability of model checking for some properties which cannot be expressed in timed temporal logics and provide with alternative proofs of some known decidable properties. Our proof relies on two intermediate results: 1. Every timed automaton can be effectively emulated by a timed automaton which does not contain nested loops. 2. The binary reachability relation for counter automata without nested loops (called here flat automata) is expressible in the additive theory of integers (resp. real numbers). The second result can be derived from [10].

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Authors and Affiliations

  1. LSV, ENS Cachan, 94235, Cachan cedex, France

    Hubert Comon & Yan Jurski

Authors
  1. Hubert Comon
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  2. Yan Jurski
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Editor information

Editors and Affiliations

  1. Department of Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten  & Sjouke Mauw  & 

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Comon, H., Jurski, Y. (1999). Timed Automata and the Theory of Real Numbers. In: Baeten, J.C.M., Mauw, S. (eds) CONCUR’99 Concurrency Theory. CONCUR 1999. Lecture Notes in Computer Science, vol 1664. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48320-9_18

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  • DOI: https://doi.org/10.1007/3-540-48320-9_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66425-3

  • Online ISBN: 978-3-540-48320-5

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