Statistical Model Checking: An Overview

  • Axel Legay
  • Benoît Delahaye
  • Saddek Bensalem
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6418)


Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical approach [31,8,35,22,21,5] that iteratively computes (or approximates) the exact measure of paths satisfying relevant subformulas; the algorithms themselves depend on the class of systems being analyzed as well as the logic used for specifying the properties. Another approach to solve the model checking problem is to simulate the system for finitely many executions, and use hypothesis testing to infer whether the samples provide a statistical evidence for the satisfaction or violation of the specification. In this tutorial, we survey the statistical approach, and outline its main advantages in terms of efficiency, uniformity, and simplicity.


Model Check Stochastic System Linear Temporal Logic Sequential Probability Ratio Test Model Check Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bauer, A., Leucker, M., Schallhart, C.: Monitoring of real-time properties. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 260–272. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Model-checking algorithms for continuous-time markov chains. IEEE Trans. Software Eng. 29(6), 524–541 (2003)CrossRefzbMATHGoogle Scholar
  3. 3.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008)zbMATHGoogle Scholar
  4. 4.
    Basu, A., Bensalem, S., Bozga, M., Caillaud, B., Delahaye, B., Legay, A.: Statistical abstraction and model-checking of large heterogeneous systems. Technical report, INRIA (2010)Google Scholar
  5. 5.
    Bustan, D., Rubin, S., Vardi, M.Y.: Verifying omega-regular properties of markov chains. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 189–201. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Carnegie Mellon University. A Bayesian Approach to Model Checking Biological Systems (under submission, 2009)Google Scholar
  7. 7.
    Ciesinski, F., Baier, C.: Liquor: A tool for qualitative and quantitative linear time analysis of reactive systems. In: QEST, pp. 131–132. IEEE, Los Alamitos (2006)Google Scholar
  8. 8.
    Ciesinski, F., Größer, M.: On probabilistic computation tree logic. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 147–188. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Clarke, E.M., Donzé, A., Legay, A.: Statistical model checking of mixed-analog circuits with an application to a third order delta-sigma modulator. In: HVC 2008. LNCS, vol. 5394, pp. 149–163. Springer, Heidelberg (2008)Google Scholar
  10. 10.
    Clarke, E.M., Donzé, A., Legay, A.: On simulation-based probabilistic model checking of mixed-analog circuits. Formal Methods in System Design (2009) (to appear)Google Scholar
  11. 11.
    Clarke, E.M., Faeder, J.R., Langmead, C.J., Harris, L.A., Jha, S.K., Legay, A.: Statistical model checking in biolab: Applications to the automated analysis of t-cell receptor signaling pathway. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 231–250. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
  13. 13.
    Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Dang, T., Donze, A., Maler, O.: Verification of analog and mixed-signal circuits using hybrid systems techniques. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 21–36. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Faeder, J.R., Blinov, M.L., Hlavacek, W.S.: Graphical rule-based representation of signal-transduction networks. In: SAC 2005: Proceedings of the 2005 ACM symposium on Applied computing, pp. 133–140. ACM, New York (2005)CrossRefGoogle Scholar
  16. 16.
    Faeder, J.R., Blinov, M.L., Hlavacek, W.S.: Rule-based modeling of biochemical systems with BioNetGen. In: Maly, I.V. (ed.) Systems Biology. Methods in Molecular Biology. Humana Press, Totowa (2008)Google Scholar
  17. 17.
    Grosu, R., Smolka, S.A.: Monte carlo model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 271–286. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  18. 18.
    Gupta, S., Krogh, B.H., Rutenbar, R.A.: Towards formal verification of analog designs. In: ICCAD, pp. 210–217 (2004)Google Scholar
  19. 19.
    Havelund, K., Rosu, G.: Synthesizing monitors for safety properties. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 342–356. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Hérault, T., Lassaigne, R., Magniette, F., Peyronnet, S.: Approximate probabilistic model checking. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 73–84. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  21. 21.
    Hermanns, H., Wachter, B., Zhang, L.: Probabilistic cegar. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 162–175. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Jansen, D.N., Katoen, J., Oldenkamp, M., Stoelinga, M., Zapreev, I.S.: How fast and fat is your probabilistic model checker? an experimental performance comparison. In: Yorav, K. (ed.) HVC 2007. LNCS, vol. 4899, pp. 69–85. Springer, Heidelberg (2008)Google Scholar
  23. 23.
    Katoen, J.-P., Zapreev, I.S.: Simulation-based ctmc model checking: An empirical evaluation. In: Proc. of 6th Int. Conference on the Quantitative Evaluation of Systems (QEST), pp. 31–40. IEEE Computer Society, Los Alamitos (2009)Google Scholar
  24. 24.
    Katoen, J.-P., Zapreev, I.S., Hahn, E.M., Hermanns, H., Jansen, D.N.: The ins and outs of the probabilistic model checker mrmc. In: Proc. of 6th Int. Conference on the Quantitative Evaluation of Systems (QEST), pp. 167–176. IEEE Computer Society Press, Los Alamitos (2009)Google Scholar
  25. 25.
    Kwiatkowska, M.Z., Norman, G., Parker, D.: Prism 2.0: A tool for probabilistic model checking. In: QEST, pp. 322–323. IEEE, Los Alamitos (2004)Google Scholar
  26. 26.
    Laplante, S., Lassaigne, R., Magniez, F., Peyronnet, S., de Rougemont, M.: Probabilistic abstraction for model checking: An approach based on property testing. ACM Trans. Comput. Log. 8(4) (2007)Google Scholar
  27. 27.
    Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94(1), 1–28 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Merayo, M.G., Hwang, I., Núñez, M., Cavalli, A.R.: A statistical approach to test stochastic and probabilistic systems. In: Breitman, K., Cavalcanti, A. (eds.) ICFEM 2009. LNCS, vol. 5885, pp. 186–205. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  29. 29.
    Pnueli, A.: The temporal logic of programs. In: Proc. 18th Annual Symposium on Foundations of Computer Science (FOCS), pp. 46–57 (1977)Google Scholar
  30. 30.
    Rabih, D.E., Pekergin, N.: Statistical model checking using perfect simulation. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 120–134. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  31. 31.
    Rutten, J., Kwiatkowska, M., Norman, G., Parker, D.: Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems. In: Panangaden, P., van Breugel, F. (eds.) Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems, P. Panangaden and F. van Breugel (eds.). CRM Monograph Series, vol. 23. American Mathematical Society, Providence (2004)CrossRefGoogle Scholar
  32. 32.
    Sen, K., Viswanathan, M., Agha, G.: Statistical model checking of black-box probabilistic systems. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 202–215. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  33. 33.
    Sen, K., Viswanathan, M., Agha, G.: On statistical model checking of stochastic systems. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 266–280. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  34. 34.
    Sen, K., Viswanathan, M., Agha, G.A.: Vesta: A statistical model-checker and analyzer for probabilistic systems. In: QEST, pp. 251–252. IEEE Computer Society, Los Alamitos (2005)Google Scholar
  35. 35.
    Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state programs. In: FOCS, pp. 327–338 (1985)Google Scholar
  36. 36.
    Wald, A.: Sequential tests of statistical hypotheses. Annals of Mathematical Statistics 16(2), 117–186 (1945)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Younes, H.L.S.: Probabilistic verification for ”black-box” systems. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 253–265. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  38. 38.
    Younes, H.L.S.: Verification and Planning for Stochastic Processes with Asynchronous Events. PhD thesis, Carnegie Mellon (2005)Google Scholar
  39. 39.
    Younes, H.L.S.: Ymer: A statistical model checker. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 429–433. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  40. 40.
    Younes, H.L.S.: Error control for probabilistic model checking. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 142–156. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  41. 41.
    Younes, H.L.S., Kwiatkowska, M.Z., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking. STTT 8(3), 216–228 (2006)CrossRefzbMATHGoogle Scholar
  42. 42.
    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
  43. 43.
    Younes, H.L.S., Simmons, R.G.: Statistical probabilistic model checking with a focus on time-bounded properties. Information and Computation 204(9), 1368–1409 (2006)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Axel Legay
    • 1
  • Benoît Delahaye
    • 1
  • Saddek Bensalem
    • 2
  1. 1.INRIA/IRISARennesFrance
  2. 2.Verimag LaboratoryUniversité Joseph Fourier Grenoble, CNRSFrance

Personalised recommendations