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On-the-fly Fast Mean-Field Model-Checking

  • Diego LatellaEmail author
  • Michele Loreti
  • Mieke Massink
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8358)

Abstract

A novel, scalable, on-the-fly model-checking procedure is presented to verify bounded PCTL properties of selected individuals in the context of very large systems of independent interacting objects. The proposed procedure combines on-the-fly model checking techniques with deterministic mean-field approximation in discrete time. The asymptotic correctness of the procedure is shown and some results of the application of a prototype implementation of the FlyFast model-checker are presented.

Keywords

Probabilistic model-checking On-the-fly model-checking Mean-field approximation Discrete time Markov chains 

References

  1. 1.
    Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model checking continuous time Markov chains. ACM Trans. Comput. Logic 1(1), 162–170 (2000)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-checking algorithms for continuous-time Markov chains. IEEE Trans. Softw. Eng. 29(6), 524–541 (2003). IEEE CSCrossRefGoogle Scholar
  3. 3.
    Bakhshi, R., Endrullis, J., Endrullis, S., Fokkink, W., Haverkort, B.: Automating the mean-field method for large dynamic gossip networks. In: QEST 2010, pp. 241–250. IEEE Computer Society (2010)Google Scholar
  4. 4.
    Benaïm, M., Le Boudec, J.Y.: A class of mean field interaction models for computer and communication systems. Perform. Eval. 65(11–12), 823–838 (2008)CrossRefGoogle Scholar
  5. 5.
    Bhat, G., Cleaveland, R., Grumberg, O.: Efficient on-the-fly model checking for CTL*. In: LICS, pp. 388–397. IEEE Computer Society (1995)Google Scholar
  6. 6.
    Bortolussi, L., Hillston, J.: Fluid model checking. In: Koutny, M., Ulidowski, I. (eds.) CONCUR. LNCS, vol. 7454, pp. 333–347. Springer, Heidelberg (2012)Google Scholar
  7. 7.
    Bortolussi, L., Hillston, J., Latella, D., Massink, M.: Continuous approximation of collective system behaviour: a tutorial. Perform. Eval. 70(5), 317–349 (2013). http://www.sciencedirect.com/science/article/pii/S0166531613000023
  8. 8.
    Bradley, J.T., Gilmore, S.T., Hillston, J.: Analysing distributed internet worm attacks using continuous state-space approximation of process algebra models. J. Comput. Syst. Sci. 74(6), 1013–1032 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Chaintreau, A., Le Boudec, J.Y., Ristanovic, N.: The age of gossip: spatial mean field regime. In: Douceur, J.R., Greenberg, A.G., Bonald, T., Nieh, J. (eds.) SIGMETRICS/Performance, pp. 109–120. ACM, Seattle (2009)Google Scholar
  10. 10.
    Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8(2), 244–263 (1986)CrossRefzbMATHGoogle Scholar
  11. 11.
    Courcoubetis, C., Vardi, M., Wolper, P., Yannakakis, M.: Memory-efficient algorithms for the verification of temporal properties. Form. Methods Syst. Des. 1(2–3), 275–288 (1992)CrossRefGoogle Scholar
  12. 12.
    Darling, R., Norris, J.: Differential equation approximations for Markov chains. Probab. Surv. 5, 37–79 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Della Penna, G., Intrigila, B., Melatti, I., Tronci, E., Zilli, M.V.: Bounded probabilistic model checking with the mur\(\varphi \) verifier. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 214–229. Springer, Heidelberg (2004)Google Scholar
  14. 14.
    Gast, N., Gaujal, B.: A mean field model of work stealing in large-scale systems. In: Misra, V., Barford, P., Squillante, M.S. (eds.) SIGMETRICS. pp. 13–24. ACM (2010)Google Scholar
  15. 15.
    Gnesi, S., Mazzanti, F.: An abstract, on the fly framework for the verification of service-oriented systems. In: Wirsing, M., Hölzl, M. (eds.) SENSORIA. LNCS, vol. 6582, pp. 390–407. Springer, Heidelberg (2011)Google Scholar
  16. 16.
    Guirado, G., Hérault, T., Lassaigne, R., Peyronnet, S.: Distribution, approximation and probabilistic model checking. Electr. Notes Theor. Comput. Sci. 135(2), 19–30 (2006). http://dx.doi.org/10.1016/j.entcs.2005.10.016
  17. 17.
    Hahn, E.M., Hermanns, H., Wachter, B., Zhang, L.: INFAMY: an infinite-state Markov model checker. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 641–647. Springer, Heidelberg (2009)Google Scholar
  18. 18.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects Comput. 6, 512–535 (1994)CrossRefzbMATHGoogle Scholar
  19. 19.
    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)Google Scholar
  20. 20.
    Holzmann, G.J.: The SPIN Model Checker: Primer and Reference Manual. Addison-Wesley, Reading (2004)Google Scholar
  21. 21.
    Kolesnichenko, A., Remke, A., de Boer, P.T.: A logic for model-checking of mean-field models. Technical report TR-CTIT-12-11. http://doc.utwente.nl/80267/ (2012)
  22. 22.
    Kolesnichenko, A., Remke, A., de Boer, P.T.: A logic for model-checking of mean-field models. In: Dependable Systems and Networks DSN13 (2013)Google Scholar
  23. 23.
    Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic symbolic model checking using PRISM: a Hybrid approach. STTT 6(2), 128–142 (2004)CrossRefGoogle Scholar
  24. 24.
    Latella, D., Loreti, M., Massink, M.: On-the-fly fast mean-field model-checking: full version. Technical report. http://arxiv.org/abs/1312.3416 (2013)
  25. 25.
    Latella, D., Loreti, M., Massink, M.: On-the-fly probabilistic model-checking: full version. Technical report. http://goo.gl/uVkPP6/ (2013)
  26. 26.
    Le Boudec, J.Y., McDonald, D., Mundinger, J.: A generic mean field convergence result for systems of interacting objects. In: QEST07. pp. 3–18. IEEE Computer Society Press (2007). ISBN 978-0-7695-2883-0Google Scholar
  27. 27.
    McCaig, C., Norman, R., Shankland, C.: From individuals to populations: a mean field semantics for process algebra. Theor. Comput. Sci. 412(17), 1557–1580 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Montes de Oca, M.A., Ferrante, E., Scheidler, A., Pinciroli, C., Birattari, M., Dorigo, M.: Majority-rule opinion dynamics with differential latency: a mechanism for self-organized collective decision-making. Swarm Intell. 5(3–4), 305–327 (2011)Google Scholar
  29. 29.
    Stefanek, A., Hayden, R.A., Bradley, J.T.: A new tool for the performance analysis of massively parallel computer systems. In: QAPL 2010. EPTCS, vol. 28. pp. 159–181 (2010)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Istituto di Scienza e Tecnologie dell’Informazione ‘A. Faedo’CNRPisaItaly
  2. 2.Università di FirenzeFirenzeItaly

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