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Statistical Model Checking of Incomplete Stochastic Systems

  • Shiraj AroraEmail author
  • Axel Legay
  • Tania Richmond
  • Louis-Marie Traonouez
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11245)

Abstract

We study incomplete stochastic systems that are missing some parts of their design, or are lacking information about some components. It is interesting to get early analysis results of the requirements of these systems, in order to adequately refine their design. In previous works, models for incomplete systems are analysed using model checking techniques for three-valued temporal logics. In this paper, we propose statistical model checking algorithms for these logics. We illustrate our approach on a case-study of a network system that is refined after the analysis of early designs.

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References

  1. 1.
    Arora, S., Rao, M.V.P.: Probabilistic model checking of incomplete models. In: Margaria, T., Steffen, B. (eds.) ISoLA 2016. LNCS, vol. 9952, pp. 62–76. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-47166-2_5CrossRefGoogle Scholar
  2. 2.
    Arora, S., Rao, M.V.P.: Probabilistic model checking of incomplete models. CoRR abs/1706.05082 (2017)Google Scholar
  3. 3.
    Bauer, A., Leucker, M., Schallhart, C.: The good, the bad, and the ugly, but how ugly is ugly? In: Sokolsky, O., Taşıran, S. (eds.) RV 2007. LNCS, vol. 4839, pp. 126–138. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-77395-5_11CrossRefzbMATHGoogle Scholar
  4. 4.
    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.) QEST 2013. LNCS, vol. 8054, pp. 160–164. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40196-1_12CrossRefGoogle Scholar
  5. 5.
    Chechik, M., Easterbrook, S., Devereux, B.: Model checking with multi-valued temporal logics. In: Proceedings of the 31st IEEE International Symposium on Multiple-Valued Logic, pp. 187–192 (2001)Google Scholar
  6. 6.
    Chechik, M., Easterbrook, S., Petrovykh, V.: Model-checking over multi-valued logics. In: Oliveira, J.N., Zave, P. (eds.) FME 2001. LNCS, vol. 2021, pp. 72–98. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-45251-6_5CrossRefGoogle Scholar
  7. 7.
    Chen, X.: Concentration inequalities for bounded random vectors. arXiv preprint: arXiv:1309.0003 (2013)
  8. 8.
    Chernoff, H.: A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Stat. 23(4), 493–507 (1952)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. J. ACM 42(4), 857–907 (1995)MathSciNetCrossRefGoogle Scholar
  10. 10.
    D’Argenio, P., Legay, A., Sedwards, S., Traonouez, L.: Smart sampling for lightweight verification of markov decision processes. STTT 17(4), 469–484 (2015)CrossRefGoogle Scholar
  11. 11.
    David, A., et al.: Statistical model checking for networks of priced timed automata. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 80–96. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-24310-3_7CrossRefGoogle Scholar
  12. 12.
    Fecher, H., Leucker, M., Wolf, V.: Don’t Know in probabilistic systems. In: Valmari, A. (ed.) SPIN 2006. LNCS, vol. 3925, pp. 71–88. Springer, Heidelberg (2006).  https://doi.org/10.1007/11691617_5CrossRefGoogle Scholar
  13. 13.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Form. Asp. Comput. 6(5), 512–535 (1994)CrossRefGoogle Scholar
  14. 14.
    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).  https://doi.org/10.1007/978-3-540-24622-0_8CrossRefzbMATHGoogle Scholar
  15. 15.
    Huth, M., Piterman, N., Wagner, D.: Three-valued abstractions of Markov chains: completeness for a sizeable fragment of PCTL. In: Kutyłowski, M., Charatonik, W., Gębala, M. (eds.) FCT 2009. LNCS, vol. 5699, pp. 205–216. Springer, Heidelberg (2009).  https://doi.org/10.1007/978-3-642-03409-1_19CrossRefzbMATHGoogle Scholar
  16. 16.
    Katoen, J.P., Klink, D., Leucker, M., Wolf, V.: Three-valued abstraction for probabilistic systems. J. Log. Algebr. Program. 81(4), 356–389 (2012). special Issue: NWPT 2009MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: verification of probabilistic real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-22110-1_47CrossRefGoogle Scholar
  18. 18.
    Legay, A., Delahaye, B., Bensalem, S.: Statistical model checking: an overview. In: Barringer, H., et al. (eds.) RV 2010. LNCS, vol. 6418, pp. 122–135. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-16612-9_11CrossRefGoogle Scholar
  19. 19.
    Legay, A., Sedwards, S., Traonouez, L.-M.: Plasma lab: a modular statistical model checking platform. In: Margaria, T., Steffen, B. (eds.) ISoLA 2016. LNCS, vol. 9952, pp. 77–93. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-47166-2_6CrossRefGoogle Scholar
  20. 20.
    Legay, A., Sedwards, S., Traonouez, L.-M.: Rare events for statistical model checking an overview. In: Larsen, K.G., Potapov, I., Srba, J. (eds.) RP 2016. LNCS, vol. 9899, pp. 23–35. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-45994-3_2CrossRefGoogle Scholar
  21. 21.
    Legay, A., Traonouez, L.-M.: Statistical model checking of simulink models with plasma lab. In: Artho, C., Ölveczky, P.C. (eds.) FTSCS 2015. CCIS, vol. 596, pp. 259–264. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-29510-7_15CrossRefGoogle Scholar
  22. 22.
    Ngo, V.C., Legay, A., Quilbeuf, J.: Statistical model checking for systemc models. In: Proceedings of HASE, pp. 197–204. IEEE Computer Society (2016)Google Scholar
  23. 23.
    Vardi, M.Y.: Automatic verification of probabilistic concurrent finite state programs. In: Proceedings of SFCS, pp. 327–338. IEEE Computer Society (1985)Google Scholar
  24. 24.
    Wald, A.: Sequential tests of statistical hypotheses. Ann. Math. Stat. 16(2), 117–186 (1945)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Younes, H.L.S.: Verification and Planning for Stochastic Processes with Asynchronous Events. Ph.D. thesis, Carnegie Mellon (2005)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Shiraj Arora
    • 1
    Email author
  • Axel Legay
    • 2
  • Tania Richmond
    • 2
  • Louis-Marie Traonouez
    • 2
  1. 1.Indian Institute of Technology HyderabadHyderabadIndia
  2. 2.InriaRennesFrance

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