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Bounded Model Checking for GSMP Models of Stochastic Real-Time Systems

  • Rajeev Alur
  • Mikhail Bernadsky
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3927)

Abstract

Model checking is a popular algorithmic verification technique for checking temporal requirements of mathematical models of systems. In this paper, we consider the problem of verifying bounded reachability properties of stochastic real-time systems modeled as generalized semi-Markov processes (GSMP). While GSMPs is a rich model for stochastic systems widely used in performance evaluation, existing model checking algorithms are applicable only to subclasses such as discrete-time or continuous-time Markov chains. The main contribution of the paper is an algorithm to compute the probability that a given GSMP satisfies a property of the form “can the system reach a target before time T within k discrete events, while staying within a set of safe states”. For this, we show that the probability density function for the remaining firing times of different events in a GSMP after k discrete events can be effectively partitioned into finitely many regions and represented by exponentials and polynomials. We report on illustrative examples and their analysis using our techniques.

Keywords

Model Check Mass Point Destination Location Discrete Event System Symbolic Model Check 
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.

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References

  1. 1.
    Alur, R., Courcoubetis, C., Dill, D.L.: Model-checking for probabilistic real-time systems. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510, pp. 115–136. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Aziz, A., Sanwal, K., Singhal, V., Brayton, R.K.: Model-checking continuous-time markov chains. ACM Transactions on Computational Logic 1(1), 162–170 (2000)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Biere, A., Cimatti, A., Clarke, E., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedures instead of BDDs. In: Proceedings of the 36th ACM/IEEE Design Automation Conference, pp. 317–320 (1999)Google Scholar
  5. 5.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press, Cambridge (2000)Google Scholar
  6. 6.
    Clarke, E.M., Kurshan, R.P.: Computer-aided verification. IEEE Spectrum 33(6), 61–67 (1996)CrossRefGoogle Scholar
  7. 7.
    Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    German, R.: Performance analysis of communication systems: Modeling with non-Markovian stochastic Petri nets. J. Wiley & Sons, Chichester (2000)MATHGoogle Scholar
  9. 9.
    Glynn, P.W.: A GSMP formalism for discrete event systems. Proceedings of the IEEE 77(1), 14–23 (1988)CrossRefGoogle Scholar
  10. 10.
    Hansson, H., Jonsson, B.: A framework for reasoning about time and reliability. In: Proceedings of the Tenth IEEE Real-Time Systems Symposium, pp. 102–111 (1989)Google Scholar
  11. 11.
    Haverkort, B.: Performance of computer-communication systems: A model-based approach. Wiley & Sons, Chichester (1998)CrossRefGoogle Scholar
  12. 12.
    Holzmann, G.J.: The model checker SPIN. IEEE Transactions on Software Engineering 23(5), 279–295 (1997)CrossRefGoogle Scholar
  13. 13.
    Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic symbolic model checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002)Google Scholar
  14. 14.
    Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Verifying quantitative properties of continuous probabilistic timed automata. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 123–137. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Kwiatkowska, M.Z.: Model checking for probability and time: from theory to pratice. In: Proceedings of the 18th IEEE Symposium on Logic in Computer Science, pp. 351–360 (2003)Google Scholar
  16. 16.
    Kwiatkowska, M.Z., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: a hybrid approach. Software Tools for Technology Transfer 6(2), 128–142 (2004)CrossRefMATHGoogle Scholar
  17. 17.
    D’Argenio, P., Hermanns, H., Katoen, J.-P., Klaren, R.: Modest - a modeling and description language for stochastic timed systems. In: de Luca, L., Gilmore, S. (eds.) PROBMIV 2001, PAPM-PROBMIV 2001, and PAPM 2001. LNCS, vol. 2165, pp. 87–104. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Shedler, G.S.: Regenerative stochastic simulation. Academic Press, London (1993)MATHGoogle Scholar
  19. 19.
    Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state programs. In: Proceedings of the 26th IEEE Symposium on Foundations of Computer Science, pp. 327–338 (1985)Google Scholar
  20. 20.
    Younes, H., Simmons, R.: Probabilistic verification of discrete event systems using acceptance sampling. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 223–235. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rajeev Alur
    • 1
  • Mikhail Bernadsky
    • 1
  1. 1.Department of Computer and Information ScienceUniversity of PennsylvaniaUSA

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