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Compositional Verification of Untimed Properties for a Class of Stochastic Automata Networks

  • Nihal PekerginEmail author
  • Minh-Anh Tran
Conference paper

Abstract

We consider Stochastic Automata Networks whose transition rates depend on the whole system state but are not synchronised and are restricted to satisfy a property called inner proportional.We prove that this class of SANs has both product form steady-state distribution and product form probability over untimed paths. This product form result is then applied to check formulae that are equivalent to some special structure that we call path-product of sets of untimed paths. In particular, we show that product form solutions can be used to check unbounded Until formulae of the Continuous Stochastic Logic.

Notes

Acknowledgments

The authors thank to Jean-Michel Fourneau for the fruitful discussions on product form solutions of SANs.

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)MathSciNetCrossRefGoogle 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)CrossRefGoogle Scholar
  3. 3.
    Baier, C, Katoen, J.-P., Hermanns, H.: Approximate symbolic model checking of continuous-time markov chains. In: CONCUR 99, LNCS 1664, pp. 146–161 (1999)Google Scholar
  4. 4.
    Ballarini, P., Horváth, A.: Compositional model checking of product-form CTMCs. Electron. Notes Theor. Comput. Sci. 250, 21–37 (2009)CrossRefGoogle Scholar
  5. 5.
    Boucherie, R.J.: A characterization of independence for competing Markov chains with applications to stochastic Petri nets. IEEE Trans. Softw. Eng. 20, 536–544 (1994)CrossRefGoogle Scholar
  6. 6.
    Buchholz, P., Katoen, J.-P., Kemper, P., Tepper, C.: Model-checking large structured Markov chains. J. Log. Algebraic Progr. 56(1–2), 69–97 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Fourneau, J.M., Plateau, B., Stewart, W.J.: An algebraic condition for product form in stochastic automata networks without synchronizations. Perform. Eval. 65, 854–868 (2008)CrossRefGoogle Scholar
  8. 8.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects Comput. 6(5), 512–535 (1994)zbMATHCrossRefGoogle Scholar
  9. 9.
    Kleinrock, L.:. Queueing Systems, volume I: Theory. Wiley Interscience, New York (1975)Google Scholar
  10. 10.
    Mamoun, M.B., Pekergin, N., Younès, S.: Model checking of continuous-time markov chains by closed-form bounding distributions. In: Third International Conference on the Quantitative Evaluation of Systems, pp. 189–198 (2006)Google Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.LACLUniversity of Paris-Est Créteil Val de MarneCréteilFrance

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