Symbolic Verification of Communicating Systems with Probabilistic Message Losses: Liveness and Fairness

  • C. Baier
  • N. Bertrand
  • Ph. Schnoebelen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4229)


NPLCS’s are a new model for nondeterministic channel systems where unreliable communication is modeled by probabilistic message losses. We show that, for ω-regular linear-time properties and finite-memory schedulers, qualitative model-checking is decidable. The techniques extend smoothly to questions where fairness restrictions are imposed on the schedulers. The symbolic procedure underlying our decidability proofs has been implemented and used to study a simple protocol handling two-way transfers in an unreliable setting.


Markov Decision Process Transition Rule Atomic Proposition Label Transition System Message Loss 
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.


  1. 1.
    Abdulla, P.A., Baier, C., Purushothaman Iyer, S., Jonsson, B.: Simulating perfect channels with probabilistic lossy channels. Information and Computation 197(1–2), 22–40 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Abdulla, P.A., Bertrand, N., Rabinovich, A., Schnoebelen, P.: Verification of probabilistic systems with faulty communication. Information and Computation 202(2), 141–165 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Abdulla, P.A., Bouajjani, A., d’Orso, J.: Deciding monotonic games. In: Baaz, M., Makowsky, J.A. (eds.) CSL 2003. LNCS, vol. 2803, pp. 1–14. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Abdulla, P.A., Collomb-Annichini, A., Bouajjani, A., Jonsson, B.: Using forward reachability analysis for verification of lossy channel systems. Formal Methods in System Design 25(1), 39–65 (2004)CrossRefzbMATHGoogle Scholar
  5. 5.
    Abdulla, P.A., Jonsson, B.: Undecidable verification problems for programs with unreliable channels. Information and Computation 130(1), 71–90 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Abdulla, P.A., Jonsson, B.: Verifying programs with unreliable channels. Information and Computation 127(2), 91–101 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Baier, C., Bertrand, N., Schnoebelen, P.: A note on the attractor-property of infinite-state Markov chains. Information Processing Letters 97(2), 58–63 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Baier, C., Bertrand, N., Schnoebelen, Ph.: On computing fixpoints in well-structured regular model checking, with applications to lossy channel systems. RR cs.CS/0606091, Computing Research Repository (June 2006), Visible at:
  9. 9.
    Baier, C., Bertrand, N., Schnoebelen, Ph.: Verifying nondeterministic probabilistic channel systems against ω-regular linear-time properties. RR cs.LO/0511023, Computing Research Repository, (April 2006); ACM Trans. Computational Logic (to be published), visible at:
  10. 10.
    Baier, C., Engelen, B.: Establishing qualitative properties for probabilistic lossy channel systems: An algorithmic approach. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, p. 34. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  11. 11.
    Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.): Validation of Stochastic Systems. LNCS, vol. 2925. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  12. 12.
    Baier, C., Kwiatkowska, M.: Model checking for a probabilistic branching time logic with fairness. Distributed Computing 11(3), 125–155 (1998)CrossRefGoogle Scholar
  13. 13.
    Bertr, N., Schnoebelen, P.: Model checking lossy channels systems is probably decidable. In: Gordon, A.D. (ed.) FOSSACS 2003. LNCS, vol. 2620, pp. 120–135. Springer, Heidelberg (2003)Google Scholar
  14. 14.
    Bertrand, N., Schnoebelen, P.: Verifying nondeterministic channel systems with probabilistic message losses. In: Bharadwaj, R. (ed.) Proc. 3rd Int. Workshop on Automated Verification of Infinite-State Systems (AVIS 2004), Barcelona, Spain (April 2004)Google Scholar
  15. 15.
    Brand, D., Zafiropulo, P.: On communicating finite-state machines. Journal of the ACM 30(2), 323–342 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Finkel, A.: Decidability of the termination problem for completely specificied protocols. Distributed Computing 7(3), 129–135 (1994)CrossRefGoogle Scholar
  18. 18.
    Hailpern, B., Owicki, S.: Verifying network protocols using temporal logic. In: Proc. NBS/IEEE Symposium on Trends and Applications 1980: Computer Network Protocols, Gaithersburg, MD, May 1980, pp. 18–28. IEEE Comp. Soc. Press, Los Alamitos (1980)Google Scholar
  19. 19.
    Hart, S., Sharir, M., Pnueli, A.: Termination of probabilistic concurrent programs. ACM Transactions on Programming Languages and Systems 5(3), 356–380 (1983)CrossRefzbMATHGoogle Scholar
  20. 20.
    Kučera, A., Schnoebelen, P.: A general approach to comparing infinite-state systems with their finite-state specifications. Theoretical Computer Science (to appear, 2006)Google Scholar
  21. 21.
    Masson, B., Schnoebelen, P.: On verifying fair lossy channel systems. In: Diks, K., Rytter, W. (eds.) MFCS 2002. LNCS, vol. 2420, pp. 543–555. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  22. 22.
    Pachl, J.K.: Protocol description and analysis based on a state transition model with channel expressions. In: Proc. 7th IFIP WG6.1 Int. Workshop on Protocol Specification, Testing, and Verification (PSTV 1987), Zurich, Switzerland, May 1987, pp. 207–219. North-Holland, Amsterdam (1987)Google Scholar
  23. 23.
    Panangaden, P.: Measure and probability for concurrency theorists. Theoretical Computer Science 253(2), 287–309 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Pnueli, A.: On the extremely fair treatment of probabilistic algorithms. In: Proc. 15th ACM Symp. Theory of Computing (STOC 1983), Boston, MA, April 1983, pp. 278–290. ACM Press, New York (1983)Google Scholar
  25. 25.
    Pnueli, A., Zuck, L.D.: Verification of multiprocess probabilistic protocols. Distributed Computing 1(1), 53–72 (1986)CrossRefzbMATHGoogle Scholar
  26. 26.
    Pnueli, A., Zuck, L.D.: Probabilistic verification. Information and Computation 103(1), 1–29 (1993)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Purushothaman Iyer, S., Narasimha, M.: Probabilistic lossy channel systems. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214, pp. 667–681. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  28. 28.
    Puterman, M.L.: Markov decision processes: discrete stochastic dynamic programming. John Wiley & Sons, Chichester (1994)CrossRefzbMATHGoogle Scholar
  29. 29.
    Rabinovich, A.: Quantitative analysis of probabilistic lossy channel systems. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1008–1021. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  30. 30.
    Schnoebelen, P.: Verifying lossy channel systems has nonprimitive recursive complexity. Information Processing Letters 83(5), 251–261 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Schnoebelen, P.: The verification of probabilistic lossy channel systems. In: Baier, et al. [11], pp. 445–465Google Scholar
  32. 32.
    Vardi, M.Y.: Automatic verification of probabilistic concurrent finite-state programs. In: Proc. 26th IEEE Symp. Foundations of Computer Science (FOCS 1985), Portland, OR, USA, October 1985, pp. 327–338. IEEE Computer Society Press, Los Alamitos (1985)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2006

Authors and Affiliations

  • C. Baier
    • 1
  • N. Bertrand
    • 2
  • Ph. Schnoebelen
    • 2
  1. 1.Universität Bonn, Institut für Informatik IGermany
  2. 2.LSV, ENS de Cachan & CNRSFrance

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