Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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)
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)
Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008)
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)
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)
Carnegie Mellon University. A Bayesian Approach to Model Checking Biological Systems (under submission, 2009)
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)
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)
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)
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)
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)
Cmacs, http://cmacs.cs.cmu.edu/
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)
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)
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)
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)
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)
Gupta, S., Krogh, B.H., Rutenbar, R.A.: Towards formal verification of analog designs. In: ICCAD, pp. 210–217 (2004)
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)
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)
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)
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)
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)
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)
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)
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)
Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94(1), 1–28 (1991)
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)
Pnueli, A.: The temporal logic of programs. In: Proc. 18th Annual Symposium on Foundations of Computer Science (FOCS), pp. 46–57 (1977)
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)
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)
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)
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)
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)
Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state programs. In: FOCS, pp. 327–338 (1985)
Wald, A.: Sequential tests of statistical hypotheses. Annals of Mathematical Statistics 16(2), 117–186 (1945)
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)
Younes, H.L.S.: Verification and Planning for Stochastic Processes with Asynchronous Events. PhD thesis, Carnegie Mellon (2005)
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)
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)
Younes, H.L.S., Kwiatkowska, M.Z., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking. STTT 8(3), 216–228 (2006)
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Legay, A., Delahaye, B., Bensalem, S. (2010). Statistical Model Checking: An Overview. In: Barringer, H., et al. Runtime Verification. RV 2010. Lecture Notes in Computer Science, vol 6418. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16612-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-16612-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-16611-2
Online ISBN: 978-3-642-16612-9
eBook Packages: Computer ScienceComputer Science (R0)