Advertisement

Bounded and Unbounded Safety Verification Using Bisimulation Metrics

  • Gang Zheng
  • Antoine Girard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5469)

Abstract

In this paper, we propose an algorithm for bounded safety verification for a class of hybrid systems described by metric transition systems. The algorithm combines exploration of the system trajectories and state space reduction using merging based on a bisimulation metric. The main novelty compared to an algorithm presented recently by Lerda et.al. lies in the introduction of a tuning parameter that makes it possible to increase the performances drastically. The second significant contribution of this work is a procedure that allows us to derive, in some cases, a proof of unbounded safety from a proof of bounded safety via a refinement step. We demonstrate the efficiency of the approach via experimental results.

Keywords

Nite 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)Google Scholar
  2. 2.
    Kapinski, J., Krogh, B., Maler, O., Stursberg, O.: On systematic simulation of open continuous systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 283–297. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Girard, A., Pappas, G.J.: Verification using simulation. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 272–286. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Donzé, A., Maler, O.: Systematic simulation using sensitivity analysis. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 174–189. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Julius, A., Fainekos, G., Anand, M., Lee, I., Pappas, G.: Robust test generation and coverage for hybrid systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 329–342. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Lerda, F., Kapinski, J., Clarke, E., Krogh, B.: Verification of supervisory control software using state proximity and merging. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 344–357. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Girard, A., Pappas, G.: Approximation metrics for discrete and continuous systems. IEEE Trans. Automatic Control 52(5), 782–798 (2007)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Weiss, G., Alur, R.: Automata based interfaces for control and scheduling. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 601–613. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  9. 9.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Gang Zheng
    • 1
  • Antoine Girard
    • 1
  1. 1.Laboratoire Jean KuntzmannUniversité de GrenobleFrance

Personalised recommendations