Faster Statistical Model Checking by Means of Abstraction and Learning

  • Ayoub Nouri
  • Balaji Raman
  • Marius Bozga
  • Axel Legay
  • Saddek Bensalem
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8734)

Abstract

This paper investigates the combined use of abstraction and probabilistic learning as a means to enhance statistical model checking performance. We are given a property (or a list of properties) for verification on a (large) stochastic system. We project on a set of traces generated from the original system, and learn a (small) abstract model from the projected traces, which contain only those labels that are relevant to the property to be verified. Then, we model-check the property on the reduced, abstract model instead of the large, original system. In this paper, we propose a formal definition of the projection on traces given a property to verify. We also provide conditions ensuring the correct preservation of the property on the abstract model. We validate our approach on the Herman’s Self Stabilizing protocol. Our experimental results show that (a) the size of the abstract model and the verification time are drastically reduced, and that (b) the probability of satisfaction of the property being verified is correctly estimated by statistical model checking on the abstract model with respect to the concrete system.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baier, C., Katoen, J.-P.: Principles of Model Checking (Representation and Mind Series). The MIT Press (2008)Google Scholar
  2. 2.
    Basu, A., Bensalem, S., Bozga, M., Bourgos, P., Maheshwari, M., Sifakis, J.: Component assemblies in the context of manycore. In: Beckert, B., Bonsangue, M.M. (eds.) FMCO 2011. LNCS, vol. 7542, pp. 314–333. Springer, Heidelberg (2012)Google Scholar
  3. 3.
    Bensalem, S., Bozga, M., Delahaye, B., Jegourel, C., Legay, A., Nouri, A.: Statistical Model Checking QoS Properties of Systems with SBIP. In: Margaria, T., Steffen, B. (eds.) ISoLA 2012, Part I. LNCS, vol. 7609, pp. 327–341. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Legay, A., Delahaye, B., Bensalem, S.: Statistical model checking: An overview. In: Barringer, H., Falcone, Y., Finkbeiner, B., Havelund, K., Lee, I., Pace, G., Roşu, G., Sokolsky, O., Tillmann, N. (eds.) RV 2010. LNCS, vol. 6418, pp. 122–135. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Bulychev, P.E., David, A., Larsen, K.G., Mikucionis, M., Poulsen, D.B., Legay, A., Wang, Z.: Uppaal-smc: Statistical model checking for priced timed automata. In: QAPL 2012, pp. 1–16 (2012)Google Scholar
  6. 6.
    Carrasco, R.C., Oncina, J.: Learning Stochastic Regular Grammars by Means of a State Merging Method. In: Carrasco, R.C., Oncina, J. (eds.) ICGI 1994. LNCS, vol. 862, pp. 139–152. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  7. 7.
    de la Higuera, C.: Grammatical Inference: Learning Automata and Grammars. Cambridge University Press, New York (2010)CrossRefGoogle Scholar
  8. 8.
    de la Higuera, C., Oncina, J.: Identification with Probability One of Stochastic Deterministic Linear Languages. In: Gavaldá, R., Jantke, K.P., Takimoto, E. (eds.) ALT 2003. LNCS (LNAI), vol. 2842, pp. 247–258. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    de la Higuera, C., Oncina, J., Vidal, E.: Identification of DFA: data-dependent vs data-independent algorithms. In: Miclet, L., de la Higuera, C. (eds.) ICGI 1996. LNCS, vol. 1147, pp. 313–325. Springer, Heidelberg (1996)Google Scholar
  10. 10.
    Denis, F., Esposito, Y., Habrard, A.: Learning rational stochastic languages. In: Lugosi, G., Simon, H.U. (eds.) COLT 2006. LNCS (LNAI), vol. 4005, pp. 274–288. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Grosu, R., Smolka, S.A.: Monte carlo model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 271–286. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Herman, T.: Probabilistic self-stabilization. Information Processing Letters 35(2), 63–67 (1990)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Hoeffding, W.: Probability inequalities. Journal of the American Statistical Association 58, 13–30 (1963)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    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)CrossRefGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    Laplante, S., Lassaigne, R., Magniez, F., Peyronnet, S., de Rougemont, M.: Probabilistic abstraction for model checking: An approach based on property testing. ACM TCS 8(4) (2007)Google Scholar
  18. 18.
    Leucker, M.: Learning Meets Verification. In: de Boer, F.S., Bonsangue, M.M., Graf, S., de Roever, W.-P. (eds.) FMCO 2006. LNCS, vol. 4709, pp. 127–151. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Mao, H., Chen, Y., Jaeger, M., Nielsen, T.D., Larsen, K.G., Nielsen, B.: Learning Probabilistic Automata for Model Checking. In: QEST, pp. 111–120 (2011)Google Scholar
  20. 20.
    Peled, D., Vardi, M.Y., Yannakakis, M.: Black box checking. J. Autom. Lang. Comb. 7(2), 225–246 (2001)MathSciNetGoogle Scholar
  21. 21.
    Pena, J.M., Oliveira, A.L.: A new algorithm for exact reduction of incompletely specified finite state machines. TCAD 18(11), 1619–1632 (2006)Google Scholar
  22. 22.
    Ron, D., Singer, Y., Tishby, N.: On the learnability and usage of acyclic probabilistic finite automata. In: COLT, pp. 31–40 (1995)Google Scholar
  23. 23.
    Sen, K., Viswanathan, M., Agha, G.: Learning continuous time markov chains from sample executions. In: QEST, pp. 146–155 (2004)Google Scholar
  24. 24.
    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)CrossRefGoogle Scholar
  25. 25.
    Stolcke, A.: Bayesian Learning of Probabilistic Language Models. PhD thesis, Berkeley, CA, USA, UMI Order No. GAX95-29515 (1994)Google Scholar
  26. 26.
    Verwer, S., Eyraud, R., de la Higuera, C.: Results of the pautomac probabilistic automaton learning competition. In: ICGI, pp. 243–248 (2012)Google Scholar
  27. 27.
    Younes, H.L.S.: Verification and Planning for Stochastic Processes with Asynchronous Events. PhD thesis, Carnegie Mellon (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Ayoub Nouri
    • 1
    • 2
  • Balaji Raman
    • 1
    • 2
  • Marius Bozga
    • 1
    • 2
  • Axel Legay
    • 3
  • Saddek Bensalem
    • 1
    • 2
  1. 1.Univ. Grenoble Alpes, VERIMAGGrenobleFrance
  2. 2.CNRS, VERIMAGGrenobleFrance
  3. 3.INRIA/IRISARennesFrance

Personalised recommendations