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Smart sampling for lightweight verification of Markov decision processes

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Abstract

Markov decision processes (MDP) are useful to model optimisation problems in concurrent systems. To verify MDPs with efficient Monte Carlo techniques requires that their nondeterminism be resolved by a scheduler. Recent work has introduced the elements of lightweight techniques to sample directly from scheduler space, but finding optimal schedulers by simple sampling may be inefficient. Here we describe “smart” sampling algorithms that can make substantial improvements in performance.

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Notes

  1. http://project.inria.fr/plasma-lab/.

  2. http://igrida.gforge.inria.fr.

  3. http://www.prismmodelchecker.org/casestudies/.

References

  1. Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008)

  2. Bellman, R.: Dynamic Programming. Princeton University Press, Princeton (1957)

  3. Bianco, A., De Alfaro, L.: Model checking of probabilistic and nondeterministic systems. In: Foundations of Software Technology and Theoretical Computer Science, pp. 499–513. Springer, New York (1995)

  4. Bogdoll, J., Fioriti, L.M.F., Hartmanns, A., Hermanns, H.: Partial order methods for statistical model checking and simulation. In: Formal Techniques for Distributed Systems, pp. 59–74. Springer, New York (2011)

  5. 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.R. (eds.) Quantitative Evaluation of Systems. LNCS, vol. 8054, pp. 160–164. Springer, New York (2013)

  6. Brázdil, T., Chatterjee, K., Chmelík, M., Forejt, V., Křetínský, J., Kwiatkowska, M., Parker, D., Ujma, M.: Verification of Markov decision processes using learning algorithms. In: Cassez, F., Raskin, J.-F. (eds.) Automated Technology for Verification and Analysis. Lecture Notes in Computer Science, vol. 8837, pp. 98–114. Springer, New York (2014)

  7. Clarke, E.M., Emerson, E.A., Sifakis, J.: Model checking: algorithmic verification and debugging. Commun. ACM 52(11), 74–84 (2009)

    Article  Google Scholar 

  8. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. MIT Press, Cambridge (2009)

  9. Eisner, C., Fisman, D., Havlicek, J., Lustig, Y., McIsaac, A., Van Campenhout D.: Reasoning with temporal logic on truncated paths. In: Computer Aided Verification, pp. 27–39. Springer, New York (2003)

  10. Geilen, M.C.W.: On the construction of monitors for temporal logic properties. Electron. Notes Theor. Comput. Sci. 55(2), 181–199 (2001)

    Article  Google Scholar 

  11. Gerth, R., Peled, D., Vardi, M.Y., Wolper, P.: Simple on-the-fly automatic verification of linear temporal logic. In: Protocol Specification Testing and Verification, pp. 3–18. Chapman & Hall, London (1995)

  12. Giannakopoulou, D., Havelund, K.: Automata-based verification of temporal properties on running programs. In: Proceedings of 16th Annual International Conference on Automated Software Engineering (ASE’01), pp. 412–416. IEEE (2001)

  13. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Form. Asp. Comput. 6(5), 512–535 (1994)

  14. Hartmanns, A., Timmer, M.: On-the-fly confluence detection for statistical model checking. In: NASA Formal Methods, pp. 337–351. Springer, New York (2013)

  15. Henriques, D., Martins, J.G., Zuliani, P., Platzer, A., Clarke Edmund, M.: Statistical model checking for Markov decision processes. In: Ninth International Conference on Quantitative Evaluation of Systems, pp. 84–93. IEEE (2012)

  16. Hoeffding, W.: Probability inequalities for sums of bounded random variables. J. Am. Stat. Assoc. 58(301), 13–30 (1963)

  17. Horner, W.G.: A new method of solving numerical equations of all orders, by continuous approximation. Philos. Trans. R. Soc. Lond. 109, 308–335 (1819)

  18. Israeli, A., Jalfon, M.: Token management schemes and random walks yield self-stabilizating mutual exclusion. In: Proceedings of 9th Annual ACM Symposium on Principles of Distributed Computing (PODC’90), pp. 119–131. ACM, New York (1990)

  19. Kearns, M., Mansour, Y., Ng, A.Y.: A sparse sampling algorithm for near-optimal planning in large Markov decision processes. Mach. Learn. 49(2–3), 193–208 (2002)

  20. Knuth, D.E.: The Art of Computer Programming, 3rd edn. Addison-Wesley, Menlo Park (1998)

  21. Kwiatkowska, M., Norman, G., Parker D.: Stochastic model checking. In: Bernardo, M., Hillston, J. (eds.) Formal Methods for the Design of Computer, Communication and Software Systems: Performance Evaluation (SFM’07). LNCS (Tutorial Volume), vol. 4486, pp. 220–270. Springer, New York (2007)

  22. Kwiatkowska, M., Norman, G., Parker, D.: Analysis of a gossip protocol in PRISM. SIGMETRICS Perform. Eval. Rev. 36(3), 17–22 (2008)

  23. Kwiatkowska, M., Norman, G., Parker, D., Sproston, J.: Performance analysis of probabilistic timed automata using digital clocks. Formal Methods in System Design 29, 33–78 (2006)

  24. Kwiatkowska, M., Norman, G., Parker, D., Vigliotti, M.G.: Probabilistic mobile ambients. Theor. Comput. Sci. 410(12–13), 1272–1303 (2009)

  25. Kwiatkowska, M.Z., Norman, G., Sproston, J.: Probabilistic model checking of the IEEE 802.11 wireless local area network protocol. In: Proceedings of \(2{\rm {nd}}\) Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification, pp. 169–187. Springer, New York (2002)

  26. Lassaigne, R., Peyronnet, S.: Approximate planning and verification for large Markov decision processes. In: Proceedings of \(27{\rm th}\) Annual ACM Symposium on Applied Computing, pp. 1314–1319. ACM, New York (2012)

  27. Legay, A., Sedwards, S., Traonouez, L.-M.: Scalable verification of Markov decision processes. In: 4th Workshop on Formal Methods in the Development of Software (FMDS’14), LNCS. Springer, New York (2014)

  28. Manna, Z., Pnueli, A.: Temporal Verification of Reactive Systems: Safety, vol. 2. Springer, New York (1995)

  29. Ndukwu, U., McIver, A.: An expectation transformer approach to predicate abstraction and data independence for probabilistic programs. In: Proceedings of 8th Workshop on Quantitative Aspects of Programming Languages (QAPL’10) (2010)

  30. Okamoto, M.: Some inequalities relating to the partial sum of binomial probabilities. Ann. Inst. Stat. Math. 10(1), 29–35 (1958)

  31. Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley-Interscience, USA (1994)

  32. Wald, A.: Sequential tests of statistical hypotheses. Ann. Math. Stat.16(2), 117–186 (1945)

  33. White, D.J.: Real applications of Markov decision processes. Interfaces 15(6), 73–83 (1985)

  34. White, D.J.: Further real applications of Markov decision processes. Interfaces 18(5), 55–61 (1988)

  35. White, D.J.: A survey of applications of Markov decision processes. J. Oper. Res. Soc. 44(11), 1073–1096 (1993)

  36. Younes, H.L.S.: Verification and planning for stochastic processes with asynchronous events. PhD thesis, Carnegie Mellon University, Pittsburgh (2005)

  37. Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: Computer Aided Verification, pp. 223–235. Springer, New York (2002)

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Acknowledgments

We are grateful to Benoît Delahaye for useful prior discussions. This work was partially supported by the European Union Seventh Framework Programme under Grant Agreement No. 295261 (MEALS).

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Authors and Affiliations

  1. Universidad Nacional de Córdoba, Córdoba, Argentina

    Pedro D’Argenio

  2. Inria Rennes-Bretagne Atlantique, Rennes, France

    Axel Legay, Sean Sedwards & Louis-Marie Traonouez

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  1. Pedro D’Argenio
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  2. Axel Legay
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  3. Sean Sedwards
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  4. Louis-Marie Traonouez
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Correspondence to Axel Legay.

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D’Argenio, P., Legay, A., Sedwards, S. et al. Smart sampling for lightweight verification of Markov decision processes. Int J Softw Tools Technol Transfer 17, 469–484 (2015). https://doi.org/10.1007/s10009-015-0383-0

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