Model-Checking and Simulation for Stochastic Timed Systems

  • Arnd Hartmanns
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6957)

Abstract

For verification and performance evaluation, system models that can express stochastic as well as real-time behaviour are of increasing importance. Although an integrated stochastic-timed verification procedure is highly desirable, both model-checking and simulation currently fall short of providing a complete, fully automatic verification solution. For model-checking, the problem lies in the extreme expressiveness of such a model, while simulation is limited to stochastic processes and cannot deal with nondeterminism. In this paper, we review the use of stochastic timed automata as an overarching formalism to model stochastic timed systems and present two analysis approaches: Model-checking for the (large) subset corresponding to probabilistic timed automata with deadlines, for which solid implementations are appearing, and simulation, which we have recently shown to be applicable to models that also include spurious nondeterministic choices.

Keywords

Model Check Stochastic Game Parallel Composition Symbolic Model Check Partial Order Reduction 
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.
    Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Baier, C., D’Argenio, P.R., Größer, M.: Partial order reduction for probabilistic branching time. Electr. Notes Theor. Comput. Sci. 153(2), 97–116 (2006)CrossRefGoogle Scholar
  3. 3.
    Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.P.: Performance evaluation and model checking join forces. Commun. ACM 53(9), 76–85 (2010)CrossRefGoogle Scholar
  4. 4.
    Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)MATHGoogle Scholar
  5. 5.
    Basu, A., Bensalem, S., Bozga, M., Caillaud, B., Delahaye, B., Legay, A.: Statistical abstraction and model-checking of large heterogeneous systems. In: Hatcliff, J., Zucca, E. (eds.) FMOODS/FORTE 2010. LNCS, vol. 6117, pp. 32–46. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Bogdoll, J., Ferrer Fioriti, L.M., Hartmanns, A., Hermanns, H.: Partial order methods for statistical model checking and simulation. In: Bruni, R., Dingel, J. (eds.) FMOODS/FORTE 2011. LNCS, vol. 6722, pp. 59–74. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Bohnenkamp, H.C., D’Argenio, P.R., Hermanns, H., Katoen, J.P.: MoDeST: A compositional modeling formalism for hard and softly timed systems. IEEE Transactions on Software Engineering 32(10), 812–830 (2006)CrossRefGoogle Scholar
  8. 8.
    Bornot, S., Sifakis, J.: An algebraic framework for urgency. Inf. Comput. 163(1), 172–202 (2000)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Cavin, D., Sasson, Y., Schiper, A.: On the accuracy of MANET simulators. In: POMC, pp. 38–43. ACM, New York (2002)CrossRefGoogle Scholar
  10. 10.
    Daws, C., Kwiatkowska, M.Z., Norman, G.: Automatic verification of the IEEE 1394 root contention protocol with KRONOS and PRISM. STTT 5(2-3), 221–236 (2004)CrossRefGoogle Scholar
  11. 11.
    Eisentraut, C., Hermanns, H., Zhang, L.: On probabilistic automata in continuous time. In: LICS, pp. 342–351. IEEE Computer Society, Los Alamitos (2010)Google Scholar
  12. 12.
    Glynn, P.W.: A GSMP formalism for discrete event systems. Proceedings of the IEEE 77, 14–23 (1989)CrossRefGoogle Scholar
  13. 13.
    Godefroid, P.: Partial-Order Methods for the Verification of Concurrent Systems – An Approach to the State-Explosion Problem. LNCS, vol. 1032. Springer, Heidelberg (1996)CrossRefMATHGoogle Scholar
  14. 14.
    Gómez, R.: A compositional translation of timed automata with deadlines to uppaal timed automata. In: Ouaknine, Vaandrager (eds.) [23], pp. 179–194Google Scholar
  15. 15.
    Grimmet, G., Stirzaker, D.: Probability and Random Processes, 3rd edn. Oxford University Press, Oxford (2001)Google Scholar
  16. 16.
    Hartmanns, A., Hermanns, H.: A Modest approach to checking probabilistic timed automata. In: QEST, pp. 187–196. IEEE Computer Society, Los Alamitos (2009)Google Scholar
  17. 17.
    Hermanns, H.: Interactive Markov Chains: The Quest for Quantified Quality. LNCS, vol. 2428. Springer, Heidelberg (2002)MATHGoogle Scholar
  18. 18.
    Kwiatkowska, M.Z., Norman, G., Parker, D.: Stochastic games for verification of probabilistic timed automata. In: Ouaknine, Vaandrager (eds.) [23], pp. 212–227Google Scholar
  19. 19.
    Kwiatkowska, M.Z., Norman, G., Parker, D., Sproston, J.: Performance analysis of probabilistic timed automata using digital clocks. Formal Methods in System Design 29(1), 33–78 (2006)CrossRefMATHGoogle Scholar
  20. 20.
    Kwiatkowska, M.Z., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. Theor. Comput. Sci. 282(1), 101–150 (2002)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Kwiatkowska, M.Z., Norman, G., Sproston, J., Wang, F.: Symbolic model checking for probabilistic timed automata. Inf. Comput. 205(7), 1027–1077 (2007)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Minea, M.: Partial order reduction for model checking of timed automata. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 431–446. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  23. 23.
    Ouaknine, J., Vaandrager, F.W. (eds.): FORMATS 2009. LNCS, vol. 5813. Springer, Heidelberg (2009)MATHGoogle Scholar
  24. 24.
    Parker, D.: Implementation of Symbolic Model Checking for Probabilistic Systems. Ph.D. thesis, University of Birmingham (2002)Google Scholar
  25. 25.
    Peled, D.: Combining partial order reductions with on-the-fly model-checking. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 377–390. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  26. 26.
    Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons Inc., New York (1994)CrossRefMATHGoogle Scholar
  27. 27.
    Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. Ph.D. thesis, MIT, Cambridge, MA, USA (1995)Google Scholar
  28. 28.
    Valmari, A.: A stubborn attack on state explosion. In: Clarke, E.M., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 156–165. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  29. 29.
    Younes, H.L.S., Kwiatkowska, M.Z., Norman, G., Parker, D.: Numerical vs. Statistical probabilistic model checking: An empirical study. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 46–60. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  30. 30.
    Younes, H.L.S., Simmons, R.G.: 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
  31. 31.
    Zhang, L., Neuhäußer, M.R.: Model checking interactive markov chains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 53–68. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  32. 32.
    Zuliani, P., Platzer, A., Clarke, E.M.: Bayesian statistical model checking with application to simulink/stateflow verification. In: Johansson, K.H., Yi, W. (eds.) HSCC, pp. 243–252. ACM, New York (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Arnd Hartmanns
    • 1
  1. 1.Computer ScienceSaarland UniversitySaarbrückenGermany

Personalised recommendations