Efficient scaling-invariant checking of timed bisimulation

  • Carsten Weise
  • Dirk Lenzkes
Specification and Verification
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1200)


Bisimulation is an important notion for the verification of distributed systems. Timed bisimulation is its natural extension to real time systems. Timed bisimulation is known to be decidable for timed automata using the so-called region technique. We present a new, top down approach to timed bisimulation which applies the zone technique from the theory of hybrid systems. In contrast to the original decision algorithm, our method has a better space complexity and is scaling invariant: altering the time scale does not effect the space complexity.


algorithms and data structures automata and formal languages program specification and verification decidability real-time systems 


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  1. [ACD93]
    R. Alur, C. Courcoubetis, D. Dill. Modelchecking in dense real-time. Information and Computation, 104(1):2–34, May 1993.CrossRefGoogle Scholar
  2. [AC+95]
    R. Alur,C. Courcoubetis, N. Halbwachs, T.A. Henzinger, et al. The algorithmic analysis of hybrid systems. TCS, February 1995.Google Scholar
  3. [ACH94]
    R. Alur, C. Courcoubetis, T.A. Henzinger. The observational power of clocks. CONCUR 94, LNCS 836, Springer 1994, pp. 162–177.Google Scholar
  4. [AD94]
    R. Alur, D.L. Dill. A Theory of Timed Automata. in: Theoretical Computer Science Vol. 126, No. 2, April 1994, pp. 183–236.CrossRefGoogle Scholar
  5. [AHV93]
    R. Alur, T.A. Henzinger, M.Y. Vardi. Parametric real-time reasoning. Proc. 25th STOC, ACM Press 1993, pp. 592–601.Google Scholar
  6. [Čer92]
    K. Čerāns. Decidability of Bisimulation Equivalences for Parallel Timer Processes. in: Proc. CAV '92, LNCS 663, pp. 302–315.Google Scholar
  7. [CGL93]
    K. Čerāns, J.C. Godsken, K.G. Larsen. Timed Modal Specification — Theory and Tools. in: Proc. CAV '93, LNCS 697, pp. 253–267.Google Scholar
  8. [Dil89]
    D.L. Dill. Timing Assumptions and Verification of Finite-State Concurrent Systems. in: LNCS 407, Springer Berlin 1989, pp. 197–212.Google Scholar
  9. [HKV96]
    T.A. Henzinger, O. Kupferman, M.Y. Vardi. A Space-Efficient On-the-fly Algorithm for Real-Time Model Checking. in: Proc. CONCUR 96.Google Scholar
  10. [HNSY92]
    T.A. Henzinger, X. Nicollin, J. Sifakis, S. Yovine. Symbolic Model Checking for Real-time Systems. LICS '92, pp. 1–13.Google Scholar
  11. [LY93]
    D. Lee, M. Yannakakis. An efficient algorithm or minimizing real-time transition systems. CAV '93, LNCS 697, Springer Berlin 1993, pp. 210–223.Google Scholar
  12. [LSW95]
    K.G. Larsen, B. Steffen, C. Weise. Fischer's Protocol Revisited: A Simple Proof Using Modal Constraints. in: LNCS 1066, Springer 1996.Google Scholar
  13. [LV91]
    N. Lynch, F. Vaandrager. Forward and Backward Simulations for Timing-Based Systems. in: REX Workshop, LNCS 600, pp. 397–446, 1991.Google Scholar
  14. [Mil89]
    R. Milner. Communication and Concurrency. Prentice-Hall, 1989.Google Scholar
  15. [NSY93]
    X. Nicollin, J. Sifakis, S. Yovine. From ATP to Timed Graphs and Hybrid Systems. Acta Informatica 30, 1993, S. 181–202.CrossRefGoogle Scholar
  16. [WL96]
    C. Weise, D. Lenzkes. A Fast Decision Algorithm for Timed Refinement. AIB 96-11, Technical Report University of Tech. Aachen, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Carsten Weise
    • 1
  • Dirk Lenzkes
    • 1
  1. 1.Lehrstuhl für Informatik IAachen University of TechnologyGermany

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