Abstract
Numerical analysis based on uniformisation and statistical techniques based on sampling and simulation are two distinct approaches for transient analysis of stochastic systems. We compare the two solution techniques when applied to the verification of time-bounded until formulae in the temporal stochastic logic CSL. This study differs from most previous comparisons of numerical and statistical approaches in that CSL model checking is a hypothesis testing problem rather than a parameter estimation problem. We can therefore rely on highly efficient sequential acceptance sampling tests, which enables statistical solution techniques to quickly return a result with some uncertainty. This suggests that statistical techniques can be useful as a first resort during system prototyping, rather than as a last resort as often suggested. We also propose a novel combination of the two solution techniques for verifying CSL queries with nested probabilistic operators.
Supported in part by DARPA and ARO under contract no. DAAD19–01–1–0485, a grant from the Royal Swedish Academy of Engineering Sciences (IVA), FORWARD and EPSRC grants GR/N22960, GR/S11107 and GR/S46727.
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Keywords
- Model Check
- Sample Path
- Binary Decision Diagram
- Sequential Probability Ratio Test
- Numerical Solution Method
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References
Alur, R., Henzinger, T.A.: Reactive modules. Formal Methods in System Design 15(1), 7–48 (1999)
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Verifying continuous time Markov chains. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 269–276. Springer, Heidelberg (1996)
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model-checking continuoustime Markov chains. ACM Transactions on Computational Logic 1(1), 162–170 (2000)
Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Model checking continuous-time Markov chains by transient analysis. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 358–372. Springer, Heidelberg (2000)
Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Model-checking algorithms for continuous-time Markov chains. IEEE Transactions on Software Engineering 29(6), 524–541 (2003)
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers C-35(8), 677–691 (1986)
Buchholz, P.: A new approach combining simulation and randomization for the analysis of large continuous time Markov chains. ACM Transactions on Modeling and Computer Simulation 8(2), 194–222 (1998)
Fox, B.L., Glynn, P.W.: Computing Poisson probabilities. Communications of the ACM 31(4), 440–445 (1988)
Fujita, M., McGeer, P.C., Yang, J.C.-Y.: Multi-terminal binary decision diagrams: An efficient data structure for matrix representation. Formal Methods in System Design 10(2/3), 149–169 (1997)
Haverkort, B.R., Hermanns, H., Katoen, J.-P.: On the use of model checking techniques for dependability evaluation. In: Proc. 19th IEEE Symposium on Reliable Distributed Systems, pp. 228–237. IEEE Computer Society, Los Alamitos (2000)
Hermanns, H., Meyer-Kayser, J., Siegle, M.: Multi terminal binary decision diagrams to represent and analyse continuous time Markov chains. In: Proc. 3rd International Workshop on the Numerical Solution of Markov Chains, pp. 188–207. Prensas Universitarias de Zaragoza (1999)
Ibe, O.C., Trivedi, K.S.: Stochastic Petri net models of polling systems. IEEE Journal on Selected Areas in Communications 8(9), 1649–1657 (1990)
Infante López, G.G., Hermanns, H., Katoen, J.-P.: Beyond memoryless distributions: Model checking semi-Markov chains. In: de Luca, L., Gilmore, S. (eds.) PROBMIV 2001, PAPM-PROBMIV 2001, and PAPM 2001. LNCS, vol. 2165, pp. 57–70. Springer, Heidelberg (2001)
Jensen, A.: Markoff chains as an aid in the study of Markoff processes. Skandinavisk Aktuarietidskrift 36, 87–91 (1953)
Katoen, J.-P., Kwiatkowska, M., Norman, G., Parker, D.: Faster and symbolic CTMC model checking. In: de Luca, L., Gilmore, S. (eds.) PROBMIV 2001, PAPM-PROBMIV 2001, and PAPM 2001. LNCS, vol. 2165, pp. 23–38. Springer, Heidelberg (2001)
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)
Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: A hybrid approach. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 52–66. Springer, Heidelberg (2002)
Malhotra, M., Muppala, J.K., Trivedi, K.S.: Stiffness-tolerant methods for transient analysis of stiff Markov chains. Microelectronics and Reliability 34(11), 1825–1841 (1994)
Parker, D.: Implementation of Symbolic Model Checking for Probabilistic Systems. PhD thesis, University of Birmingham (2002)
Reibman, A., Trivedi, K.S.: Numerical transient analysis of Markov models. Computers & Operations Research 15(1), 19–36 (1988)
Shanthikumar, J.G., Sargent, R.G.: A unifying view of hybrid simulation/ analytic models and modeling. Operations Research 31(6), 1030–1052 (1983)
Stewart, W.J.: A comparison of numerical techniques in Markov modeling. Communications of the ACM 21(2), 144–152 (1978)
Tiechroew, D., Lubin, J.F.: Computer simulation—discussion of the techniques and comparison of languages. Communications of the ACM 9(10), 723–741 (1966)
Wald, A.: Sequential tests of statistical hypotheses. Annals of Mathematical Statistics 16(2), 117–186 (1945)
Younes, H.L.S., Musliner, D.J., Simmons, R.G.: A framework for planning in continuous-time stochastic domains. In: Proc. Thirteenth International Conference on Automated Planning and Scheduling, pp. 195–204. AAAI Press, Menlo Park (2003)
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)
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Younes, H.L.S., Kwiatkowska, M., Norman, G., Parker, D. (2004). Numerical vs. Statistical Probabilistic Model Checking: An Empirical Study. In: Jensen, K., Podelski, A. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2004. Lecture Notes in Computer Science, vol 2988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24730-2_4
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DOI: https://doi.org/10.1007/978-3-540-24730-2_4
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