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International Symposium on Leveraging Applications of Formal Methods

ISoLA 2018: Leveraging Applications of Formal Methods, Verification and Validation. Verification pp 354–371Cite as

Statistical Model Checking of Incomplete Stochastic Systems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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. 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_5

    Chapter  Google Scholar 

  2. Arora, S., Rao, M.V.P.: Probabilistic model checking of incomplete models. CoRR abs/1706.05082 (2017)

    Google Scholar 

  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_11

    Chapter  MATH  Google Scholar 

  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_12

    Chapter  Google Scholar 

  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. 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_5

    Chapter  Google Scholar 

  7. Chen, X.: Concentration inequalities for bounded random vectors. arXiv preprint: arXiv:1309.0003 (2013)

  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)

    Article  MathSciNet  Google Scholar 

  9. Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. J. ACM 42(4), 857–907 (1995)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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_7

    Chapter  Google Scholar 

  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_5

    Chapter  Google Scholar 

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

    Article  Google Scholar 

  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_8

    Chapter  MATH  Google Scholar 

  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_19

    Chapter  MATH  Google Scholar 

  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 2009

    Article  MathSciNet  Google Scholar 

  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_47

    Chapter  Google Scholar 

  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_11

    Chapter  Google Scholar 

  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_6

    Chapter  Google Scholar 

  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_2

    Chapter  Google Scholar 

  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_15

    Chapter  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  25. Younes, H.L.S.: Verification and Planning for Stochastic Processes with Asynchronous Events. Ph.D. thesis, Carnegie Mellon (2005)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Indian Institute of Technology Hyderabad, Hyderabad, India

    Shiraj Arora

  2. Inria, Rennes, France

    Axel Legay, Tania Richmond & Louis-Marie Traonouez

Authors
  1. Shiraj Arora
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  2. Axel Legay
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  3. Tania Richmond
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  4. Louis-Marie Traonouez
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Corresponding author

Correspondence to Shiraj Arora .

Editor information

Editors and Affiliations

  1. University of Limerick, Limerick, Ireland

    Tiziana Margaria

  2. TU Dortmund, Dortmund, Germany

    Bernhard Steffen

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Arora, S., Legay, A., Richmond, T., Traonouez, LM. (2018). Statistical Model Checking of Incomplete Stochastic Systems. In: Margaria, T., Steffen, B. (eds) Leveraging Applications of Formal Methods, Verification and Validation. Verification. ISoLA 2018. Lecture Notes in Computer Science(), vol 11245. Springer, Cham. https://doi.org/10.1007/978-3-030-03421-4_23

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  • DOI: https://doi.org/10.1007/978-3-030-03421-4_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-03420-7

  • Online ISBN: 978-3-030-03421-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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