A Proof System for Timed Automata

  • Huimin Lin
  • Wang Yi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1784)

Abstract

A proof system for timed automata is presented, based on a CCS-style language for describing timed automata. It consists of the standard monoid laws for bisimulation and a set of inference rules. The judgments of the proof system are conditional equations of the form φt = u where φ is a clock constraint and t, u are terms denoting timed automata. It is proved that the proof system is complete for timed bisimulation over the recursion-free subset of the language. The completeness proof relies on the notion of symbolic timed bisimulation. The axiomatisation is also extended to handle an important variation of timed automata where each node is associated with an invariant constraint.

References

  1. [AD94]
    R. Alur and D.L. Dill. A theory of timed automata. Theoretical Computer Science, 126:183–235, 1994.MATHCrossRefMathSciNetGoogle Scholar
  2. [AJ94]
    L. Aceto and A. Jeffrey. A complete axiomatization of timed bisimulation for a class of timed regular behaviours. Report 4/94, Sussex University, 1994.Google Scholar
  3. [Bor96]
    M. Boreale. Symbolic Bisimulation for Timed Processes. In AMAST’96, LNCS 1101 pp.321–335. Springer-Verlag. 1996.Google Scholar
  4. [Cer92]
    K. Čeräns. Decidability of Bisimulation Equivalences for Parallel Timer Processes. In CAV’92, LNCS 663, pp.302–315. Springer-Verlag. 1992.Google Scholar
  5. [DAB96]
    P.R. D’Argenio and Ed Brinksma. A Calculus for Timed Automata (Extended Abstract). In FTRTFTS’96, LNCS 1135, pp.110–129. Springer-Verlag. 1996.Google Scholar
  6. [HL95]
    M. Hennessy and H. Lin. Symbolic bisimulations. Theoretical Computer Science, 138:353–389, 1995.MATHCrossRefMathSciNetGoogle Scholar
  7. [HL96]
    M. Hennessy and H. Lin. Proof systems for message-passing process algebras. Formal Aspects of Computing, 8:408–427, 1996.CrossRefGoogle Scholar
  8. [Lin94]
    H. Lin. Symbolic bisimulations and proof systems for the π-calculus. Report 7/94, Computer Science, University of Sussex, 1994.Google Scholar
  9. [Mil84]
    R. Milner. A complete inference system for a class of regular behaviours. J. Computer and System Science, 28:439–466, 1984.MATHCrossRefMathSciNetGoogle Scholar
  10. [Mil89]
    R. Milner. Communication and Concurrency. Prentice-Hall, 1989.Google Scholar
  11. [Wan91]
    Wang Yi. A Calculus of Real Time Systems. Ph.D. thesis, Chalmers University, 1991.Google Scholar
  12. [WPD94]
    Wang Yi, Paul Pettersson, and Mats Daniels. Automatic Verification of Real-Time Communicating Systems By Constraint-Solving. In Proc. of the 7th International Conference on Formal Description Techniques, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Huimin Lin
    • 1
  • Wang Yi
    • 2
  1. 1.Laboratory for Computer Science, Institute of SoftwareChinese Academy of SciencesChinese
  2. 2.Department of Computer SystemsUppsala UniversityUppsala

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