Dynamical properties of timed automata

  • Anuj Puri
Selected Presentations Model Checking
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1486)


Timed automata are an important model for specifying and analyzing real-time systems. The main analysis performed on timed automata is the reachability analysis. In this paper we show that the standard approach for performing reachability analysis is not correct when the clocks drift even by a very small amount. Our formulation of the reachability problem for timed automata is as follows: we define the set R *(T,Z 0) = ∩>0Reach(T ,Z 0) where T is obtained from timed automaton T by allowing an ε drift in the clocks. R *(T, Z 0) is the set of states which can be reached in the timed automaton T from the initial states in Z 0 when the clocks drift by an infinitesimally small amount. We present an algorithm for computing R *(T, Z 0) and provide a proof of its correctness. We show that R *(T, Z 0) is robust with respect to various types of modeling errors. To prove the correctness of our algorithm, we need to understand the dynamics of timed automata — in particular, the structure of the limit cycles of timed automata.


Timed Automata Dynamical Systems Verification 


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  1. 1.
    R. Alur and D. Dill, Automata for modeling real-time systems, Proc. 17th ICALP, LNCS 443, Springer-Verlag, 1990.Google Scholar
  2. 2.
    R. Alur et. al., The algorithmic analysis of hybrid systems, Theoretical Computer Science, Feb. 1995.Google Scholar
  3. 3.
    R. Alur, A. Itai, R. Kurshan and M. Yannakakis, Timing verification by successive approximation, Information and Computation 118, 142–157, 1995.MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    R. Alur and R. Kurshan, Timing analysis in COSPAN, Hybrid Systems III, LNCS 1066, Springer-Verlag, 1996.Google Scholar
  5. 5.
    J. Bengtsson, K. G. Larsen, F. Larsson, P. Pettersson and W. Yi, UppAal: a toolsuite for automatic verification of real-time systems, Hybrid Systems III, LNCS 1066, Springer-Verlag, 1996.Google Scholar
  6. 6.
    T.H. Cormen, C.E. Leiserson and R.L. Rivest Introduction to Algorithms, MIT Press, 1990.Google Scholar
  7. 7.
    C. Courcoubetis and M. Yannakakis, Minimum and maximum delay problems in real-time systems, Formal Methods in System Design, Dec. 1992, vol. 1, pp. 385–415.MATHCrossRefGoogle Scholar
  8. 8.
    C. Daws, A. Olivero, S. Tripakis and S. Yovine, The tool Kronos, Hybrid Systems III, LNCS 1066, Springer-Verlag, 1996.Google Scholar
  9. 9.
    D. Dill, Timing assumptions and verification of finite state concurrent systems, Automatic Verification Methods for Finite-State Systems, Springer-Verlag LNCS 407, 1989.Google Scholar
  10. 10.
    T. Henzinger, P.-H. Ho and H. Wong-Toi, HyTech: A model checker for hybrid systems, Computer Aided Verification, LNCS 1254, Springer-Verlag, 1997.Google Scholar
  11. 11.
    T. Henzinger, P. Kopke, A. Puri and P. Varaiya, What’s decidable about hybrid automata?, Proc. 27th ACM Symp. on Theory of Computing, 1995.Google Scholar
  12. 12.
    T. Henzinger, X. Nicollin, J. Sifakis and S. Yovine, Symbolic model-checking for real-time systems, Proc. 7th IEEE Symp. on Logic in Computer Science, 1992.Google Scholar
  13. 13.
    M. W. Hirsh and S. Smale Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, Inc., 1974.Google Scholar
  14. 14.
    A. Puri and P. Varaiya, Decidable hybrid systems, Computer and Mathematical Modeling, June 1996, vol. 23, 191–202.MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    A. Puri, Theory of hybrid systems and discrete event systems, PhD thesis, University of California, Berkeley, 1995.Google Scholar
  16. 16.
    A. Puri, Dynamical Properties of Timed Automata, Bell Labs Technical Memo, August, 1997.Google Scholar
  17. 17.
    M. Yannakakis and D. Lee, An efficient algorithm for minimizing real-time transition systems, Computer Aided Verification, Springer-Verlag, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Anuj Puri
    • 1
  1. 1.Bell LaboratoriesMurray Hill

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