Abstract
Statistical model checking avoids the intractable growth of states associated with numerical model checking by estimating the probability of a property from simulations. Rare properties pose a challenge because the relative error of the estimate is unbounded. In [13] we describe how importance splitting may be used with SMC to overcome this problem. The basic idea is to decompose a logical property into nested properties whose probabilities are easier to estimate. To improve performance it is desirable to decompose the property into many equi-probable levels, but logical decomposition alone may be too coarse.
In this article we make use of the notion of a score function to improve the granularity of a logical property. We show that such a score function may take advantage of heuristics, so long as it also rigorously respects certain properties. To demonstrate our importance splitting approach we present an optimal adaptive importance splitting algorithm and an heuristic score function. We give experimental results that demonstrate a significant improvement in performance over alternative approaches.
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References
Baier, C., Katoen, J.-P.: Principles of Model Checking (Representation and Mind Series). The MIT Press (2008)
Barbot, B., Haddad, S., Picaronny, C.: Coupling and importance sampling for statistical model checking. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 331–346. Springer, Heidelberg (2012)
Boyer, B., Corre, K., Legay, A., Sedwards, S.: PLASMA-lab: A flexible, distributable statistical model checking library. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P. (eds.) QEST 2013. LNCS, vol. 8054, pp. 160–164. Springer, Heidelberg (2013)
Cérou, F., Del Moral, P., Furon, T., Guyader, A.: Sequential Monte Carlo for rare event estimation. Statistics and Computing 22, 795–808 (2012)
Cérou, F., Guyader, A.: Adaptive multilevel splitting for rare event analysis. Stochastic Analysis and Applications 25, 417–443 (2007)
Clarke, E., Emerson, E.A., Sifakis, J.: Model checking: algorithmic verification and debugging. Commun. ACM 52(11), 74–84 (2009)
Clarke Jr., E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press, Cambridge (1999)
Del Moral, P.: Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications. Probability and Its Applications. Springer (2004)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81, 2340–2361 (1977)
Glasserman, P., Heidelberger, P., Shahabuddin, P., Zajic, T.: Multilevel splitting for estimating rare event probabilities. Oper. Res. 47(4), 585–600 (1999)
Jegourel, C., Legay, A., Sedwards, S.: A Platform for High Performance Statistical Model Checking – PLASMA. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 498–503. Springer, Heidelberg (2012)
Jegourel, C., Legay, A., Sedwards, S.: Cross-Entropy Optimisation of Importance Sampling Parameters for Statistical Model Checking. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 327–342. Springer, Heidelberg (2012)
Jegourel, C., Legay, A., Sedwards, S.: Importance splitting for statistical model checking rare properties. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 576–591. Springer, Heidelberg (2013)
Kahn, H.: Random sampling (Monte Carlo) techniques in neutron attenuation problems. Nucleonics 6(5), 27 (1950)
Kahn, H., Harris, T.E.: Estimation of Particle Transmission by Random Sampling. In: Applied Mathematics. Series 12, vol. 5. National Bureau of Standards (1951)
Kahn, H., Marshall, A.W.: Methods of Reducing Sample Size in Monte Carlo Computations. Operations Research 1(5), 263–278 (1953)
Lehmann, D., Rabin, M.O.: On the Advantage of Free Choice: A Symmetric and Fully Distributed Solution to the Dining Philosophers Problem (Extended Abstract). In: Proc. 8th Ann. Symposium on Principles of Programming Languages, pp. 133–138 (1981)
Okamoto, M.: Some inequalities relating to the partial sum of binomial probabilities. Annals of the Institute of Statistical Mathematics 10, 29–35 (1959)
Reijsbergen, D., de Boer, P.-T., Scheinhardt, W., Haverkort, B.: Rare event simulation for highly dependable systems with fast repairs. Performance Evaluation 69(7-8), 336–355 (2012)
Rosenbluth, M.N., Rosenbluth, A.W.: Monte Carlo Calculation of the Average Extension of Molecular Chains. Journal of Chemical Physics 23(2) (February 1955)
Villén-Altamirano, M., Villén-Altamirano, J.: RESTART: A Method for Accelerating Rare Event Simulations. In: Cohen, J.W., Pack, C.D. (eds.) Queueing, Performance and Control in ATM, pp. 71–76. Elsevier (1991)
Wald, A.: Sequential Tests of Statistical Hypotheses. The Annals of Mathematical Statistics 16(2), 117–186 (1945)
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Jegourel, C., Legay, A., Sedwards, S. (2014). An Effective Heuristic for Adaptive Importance Splitting in Statistical Model Checking. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. Specialized Techniques and Applications. ISoLA 2014. Lecture Notes in Computer Science, vol 8803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45231-8_11
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DOI: https://doi.org/10.1007/978-3-662-45231-8_11
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