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Error Control for Probabilistic Model Checking

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Book cover Verification, Model Checking, and Abstract Interpretation (VMCAI 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3855))

Abstract

We introduce a framework for expressing correctness guarantees of model-checking algorithms. The framework allows us to qualitatively compare different solution techniques for probabilistic model checking, both techniques based on statistical sampling and numerical computation of probability estimates. We provide several new insights into the relative merits of the different approaches. In addition, we present a new statistical solution method that can bound the probability of error under any circumstances by sometimes reporting undecided results. Previous statistical solution methods could only bound the probability of error outside of an “indifference region.”

Supported in part by the US Army Research Office (ARO), under contract no. DAAD190110485.

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References

  1. Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. 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)

    Chapter  Google Scholar 

  3. 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)

    Article  Google Scholar 

  4. Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)

    Chapter  Google Scholar 

  5. Duncan, A.J.: Quality Control and Industrial Statistics. In: Irwin, R.D. (ed.), 4th edn. (1974)

    Google Scholar 

  6. Fox, B.L., Glynn, P.W.: Computing Poisson probabilities. Communications of the ACM 31(4), 440–445 (1988)

    Article  MathSciNet  Google Scholar 

  7. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6(5), 512–535 (1994)

    Article  MATH  Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. Hermanns, H., Katoen, J.-P., Meyer-Kayser, J., Siegle, M.: A tool for model-checking Markov chains. International Journal on Software Tools for Technology Transfer 4(2), 153–172 (2003)

    Article  Google Scholar 

  10. Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58(301), 13–30 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  11. Jensen, A.: Markoff chains as an aid in the study of Markoff processes. Skandinavisk Aktuarietidskrift 36, 87–91 (1953)

    Google Scholar 

  12. Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking with PRISM: A hybrid approach. International Journal on Software Tools for Technology Transfer 6(2), 128–142 (2004)

    Article  Google Scholar 

  13. Lassaigne, R., Peyronnet, S.: Approximate verification of probabilistic systems. In: Hermanns, H., Segala, R. (eds.) PROBMIV 2002, PAPM-PROBMIV 2002, and PAPM 2002. LNCS, vol. 2399, pp. 213–214. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  14. Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, MIT-LCS-TR-676 (1995)

    Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. Wald, A.: Sequential tests of statistical hypotheses. Annals of Mathematical Statistics 16(2), 117–186 (1945)

    Article  MATH  MathSciNet  Google Scholar 

  17. Younes, H.L.S.: Verification and Planning for Stochastic Processes with Asynchronous Events. PhD thesis, Computer Science Department, Carnegie Mellon University, CMU-CS-05-105 (2005)

    Google Scholar 

  18. Younes, H.L.S., Kwiatkowska, M., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking: An empirical study. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 46–60. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  19. 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)

    Chapter  Google Scholar 

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Younes, H.L.S. (2005). Error Control for Probabilistic Model Checking. In: Emerson, E.A., Namjoshi, K.S. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2006. Lecture Notes in Computer Science, vol 3855. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11609773_10

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  • DOI: https://doi.org/10.1007/11609773_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31139-3

  • Online ISBN: 978-3-540-31622-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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