Advertisement

Hierarchical Counterexamples for Discrete-Time Markov Chains

  • Nils Jansen
  • Erika Ábrahám
  • Jens Katelaan
  • Ralf Wimmer
  • Joost-Pieter Katoen
  • Bernd Becker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6996)

Abstract

This paper introduces a novel counterexample generation approach for the verification of discrete-time Markov chains (DTMCs) with two main advantages: (1) We generate abstract counterexamples which can be refined in a hierarchical manner. (2) We aim at minimizing the number of states involved in the counterexamples, and compute a critical subsystem of the DTMC whose paths form a counterexample. Experiments show that with our approach we can reduce the size of counterexamples and the number of computation steps by several orders of magnitude.

Keywords

Local Search Model Check Target State Linear Temporal Logic Strongly Connect Component 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ábrahám, E., Jansen, N., Katelaan, J., Wimmer, R., Katoen, J.P., Becker, B.: Hierarchical counterexamples for discrete-time Markov chains. Tech. rep., RWTH Aachen University (2011), http://sunsite.informatik.rwth-aachen.de/Publications/AIB/2011/2011-11.pdf
  2. 2.
    Ábrahám, E., Jansen, N., Wimmer, R., Katoen, J.P., Becker, B.: DTMC model checking by SCC reduction. In: Proc. of QEST, pp. 37–46. IEEE CS, Los Alamitos (2010)Google Scholar
  3. 3.
    Aljazzar, H., Leue, S.: Directed explicit state-space search in the generation of counterexamples for stochastic model checking. IEEE Trans. on Software Engineering 36(1), 37–60 (2010)CrossRefGoogle Scholar
  4. 4.
    Andrés, M.E., D’Argenio, P., van Rossum, P.: Significant diagnostic counterexamples in probabilistic model checking. In: Chockler, H., Hu, A.J. (eds.) HVC 2008. LNCS, vol. 5394, pp. 129–148. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Han, T., Katoen, J.P., Damman, B.: Counterexample generation in probabilistic model checking. IEEE Trans. on Software Engineering 35(2), 241–257 (2009)CrossRefGoogle Scholar
  6. 6.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6(5), 512–535 (1994)Google Scholar
  7. 7.
    Itai, A., Rodeh, M.: Symmetry breaking in distributed networks. Information and Computation 88(1), 60–87 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Katoen, J.P., Zapreev, I.S., Hahn, E.M., Hermanns, H., Jansen, D.N.: The ins and outs of the probabilistic model checker MRMC. In: Proc. of QEST, pp. 167–176. IEEE CS, Los Alamitos (2009)Google Scholar
  9. 9.
    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
  10. 10.
    Reiter, M.K., Rubin, A.D.: Crowds: Anonymity for web transactions. ACM Trans. on Information and System Security 1(1), 66–92 (1998)CrossRefGoogle Scholar
  11. 11.
    Wimmer, R., Braitling, B., Becker, B.: Counterexample generation for discrete-time Markov chains using bounded model checking. In: Jones, N.D., Müller-Olm, M. (eds.) VMCAI 2009. LNCS, vol. 5403, pp. 366–380. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nils Jansen
    • 1
  • Erika Ábrahám
    • 1
  • Jens Katelaan
    • 1
  • Ralf Wimmer
    • 2
  • Joost-Pieter Katoen
    • 1
  • Bernd Becker
    • 2
  1. 1.RWTH Aachen UniversityGermany
  2. 2.Albert-Ludwigs-University FreiburgGermany

Personalised recommendations