Advertisement

On-the-Fly Model Checking for Extended Action-Based Probabilistic Operators

  • Radu MateescuEmail author
  • José Ignacio Requeno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9641)

Abstract

The quantitative analysis of concurrent systems requires expressive and user-friendly property languages combining temporal, data-handling, and quantitative aspects. In this paper, we aim at facilitating the quantitative analysis of systems modeled as PTSs (Probabilistic Transition Systems) labeled by actions containing data values and probabilities. We propose a new regular probabilistic operator that computes the probability measure of a path specified by a generalized regular formula involving arbitrary computations on data values. This operator, which subsumes the Until operators of PCTL and their action-based counterparts, can provide useful quantitative information about paths having certain (e.g., peak) cost values. We integrated the regular probabilistic operator into MCL (Model Checking Language) and we devised an associated on-the-fly model checking method, based on a combined local resolution of linear and Boolean equation systems. We implemented the method in the EVALUATOR model checker of the CADP toolbox and experimented it on realistic PTSs modeling concurrent systems.

Keywords

Model Check Critical Section Linear Equation System Entry Section Signal Flow Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was supported by the European project SENSATION (Self Energy-Supporting Autonomous Computation) FP7-318490.

References

  1. 1.
    Amestoy, P.R., Duff, I.S., L’Excellent, J.-Y., Koster, J.: MUMPS: a general purpose distributed memory sparse solver. In: Sørevik, T., Manne, F., Moe, R., Gebremedhin, A.H. (eds.) PARA 2000. LNCS, vol. 1947, pp. 121–130. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Andersen, H.R.: Model checking and boolean graphs. TCS 126(1), 3–30 (1994)CrossRefzbMATHGoogle Scholar
  3. 3.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008)zbMATHGoogle Scholar
  4. 4.
    Bolze, R., Cappello, F., Caron, E., Daydé, M.J., Desprez, F., Jeannot, E., Jégou, Y., Lanteri, S., Leduc, J., Melab, N., Mornet, G., Namyst, R., Primet, P., Quétier, B., Richard, O., Talbi, E.-G., Touche, I.: Grid’5000: a large scale and highly reconfigurable experimental grid testbed. IJHPCA 20(4), 481–494 (2006)Google Scholar
  5. 5.
    Brzozowski, J.A.: Derivatives of regular expressions. JACM 11(4), 481–494 (1964)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Champelovier, D., Clerc, X., Garavel, H., Guerte, Y., McKinty, C., Powazny, V., Lang, F., Serwe, W., Smeding, G.: Reference manual of the LNT to LOTOS translator (Version 6.2). Inria/Vasy and Inria/Convecs, p. 130 (2015)Google Scholar
  7. 7.
    Chua, L.O., Lin, P.M.: Computer Aided Analysis of Electronic Circuits. Prentice Hall, Upper Saddle River (1975)zbMATHGoogle Scholar
  8. 8.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)Google Scholar
  9. 9.
    Cleaveland, R., Iyer, S.P., Narasimha, M.: Probabilistic temporal logics via the modal \(\mu \)-calculus. TCS 342(2–3), 316–350 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Cleaveland, R., Steffen, B.: A linear-time model-checking algorithm for the alternation-free modal mu-calculus. FMSD 2(2), 121–147 (1993)zbMATHGoogle Scholar
  11. 11.
    Dershowitz, N.: Termination of rewriting. J. Symb. Comput. 3(1), 69–115 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Dijkstra, E.W.: Solution of a problem in concurrent programming control. CACM 8(9), 569 (1965)CrossRefGoogle Scholar
  13. 13.
    Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. JCSS 18(2), 194–211 (1979)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Garavel, H., Lang, F.: SVL: a scripting language for compositional verification. In: FORTE 2001, pp. 377–392. Kluwer (2001)Google Scholar
  15. 15.
    Garavel, H., Lang, F., Mateescu, R., Serwe, W.: CADP 2011: a toolbox for the construction and analysis of distributed processes. STTT 15(2), 89–107 (2013)CrossRefzbMATHGoogle Scholar
  16. 16.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Asp. Comput. 6(5), 512–535 (1994)CrossRefzbMATHGoogle Scholar
  17. 17.
    Kozen, D.: Results on the propositional \(\mu \)-calculus. TCS 27, 333–354 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Kozen, D.: A probabilistic PDL. JCSS 30(2), 162–178 (1985)MathSciNetzbMATHGoogle Scholar
  19. 19.
    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
  20. 20.
    Larsen, K.G.: Proof systems for hennessy-milner logic with recursion. In: Dauchet, M., Nivat, M. (eds.) CAAP 1988. LNCS, vol. 299. Springer, Heidelberg (1988)Google Scholar
  21. 21.
    Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Inf. Comput. 94(1), 1–28 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Latella, D., Loreti, M., Massink, M.: On-the-fly fast mean-field model-checking. In: Abadi, M., Lluch Lafuente, A. (eds.) TGC 2013. LNCS, vol. 8358, pp. 297–314. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  23. 23.
    Mateescu, R.: Caesar\(\_\)solve: a generic library for on-the-fly resolution of alternation-free boolean equation systems. STTT 8(1), 37–56 (2006)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Mateescu, R., Monteiro, P.T., Dumas, E., de Jong, H.: CTRL: extension of CTL with regular expressions and fairness operators to verify genetic regulatory networks. TCS 412(26), 2854–2883 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Mateescu, R., Serwe, W.: Model checking and performance evaluation with CADP illustrated on shared-memory mutual exclusion protocols. SCP 78(7), 843–861 (2013)Google Scholar
  26. 26.
    Mateescu, R., Sighireanu, M.: Efficient on-the-fly model-checking for regular alternation-free \(\mu \)-calculus. SCP 46(3), 255–281 (2003)MathSciNetzbMATHGoogle Scholar
  27. 27.
    Mateescu, R., Thivolle, D.: A model checking language for concurrent value-passing systems. In: Cuellar, J., Sere, K. (eds.) FM 2008. LNCS, vol. 5014, pp. 148–164. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  28. 28.
    R. De Nicola and F. W. Vaandrager. Action versus State Based Logics for Transition Systems. In Semantics of concurrency, LNCS vol. 469, pp. 407–419. Springer, (1990)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Inria, CNRS, LIGGrenobleFrance
  2. 2.University of Grenoble Alpes, LIGGrenobleFrance

Personalised recommendations