On the Completeness of Bounded Model Checking for Threshold-Based Distributed Algorithms: Reachability

  • Igor Konnov
  • Helmut Veith
  • Josef Widder
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8704)

Abstract

Counter abstraction is a powerful tool for parameterized model checking, if the number of local states of the concurrent processes is relatively small. In recent work, we introduced parametric interval counter abstraction that allowed us to verify the safety and liveness of threshold-based fault-tolerant distributed algorithms (FTDA). Due to state space explosion, applying this technique to distributed algorithms with hundreds of local states is challenging for state-of-the-art model checkers. In this paper, we demonstrate that reachability properties of FTDAs can be verified by bounded model checking. To ensure completeness, we need an upper bound on the diameter, i.e., on the longest distance between states. We show that the diameters of accelerated counter systems of FTDAs, and of their counter abstractions, have a quadratic upper bound in the number of local transitions. Our experiments show that the resulting bounds are sufficiently small to use bounded model checking for parameterized verification of reachability properties of several FTDAs, some of which have not been automatically verified before.

Keywords

Model Check Shared Variable Precedence Relation Counter System Abstract Domain 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    ByMC: Byzantine model checker (2013), http://forsyte.tuwien.ac.at/software/bymc/ (accessed: June 2014)
  2. 2.
    Bardin, S., Finkel, A., Leroux, J., Petrucci, L.: Fast: acceleration from theory to practice. STTT 10(5), 401–424 (2008)CrossRefGoogle Scholar
  3. 3.
    Bardin, S., Leroux, J., Point, G.: Fast extended release. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 63–66. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  4. 4.
    Basler, G., Mazzucchi, M., Wahl, T., Kroening, D.: Symbolic counter abstraction for concurrent software. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 64–78. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Biere, A.: Lingeling, Plingeling and Treengeling entering the SAT competition 2013. In: Proceedings of SAT Competition 2013; Solver and p. 51 (2013)Google Scholar
  6. 6.
    Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic model checking without bdds. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Bokor, P., Kinder, J., Serafini, M., Suri, N.: Efficient model checking of fault-tolerant distributed protocols. In: DSN, pp. 73–84 (2011)Google Scholar
  8. 8.
    Bracha, G., Toueg, S.: Asynchronous consensus and broadcast protocols. J. ACM 32(4), 824–840 (1985)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Chandra, T.D., Toueg, S.: Unreliable failure detectors for reliable distributed systems. JACM 43(2), 225–267 (1996)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Cimatti, A., Clarke, E.M., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., Sebastiani, R., Tacchella, A.: Nusmv 2: An opensource tool for symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 359–364. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Clarke, E., Kroning, D., Ouaknine, J., Strichman, O.: Completeness and complexity of bounded model checking. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 85–96. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Doeppner, T.W.: Parallel program correctness through refinement. In: POPL, pp. 155–169 (1977)Google Scholar
  13. 13.
    Gmeiner, A., Konnov, I., Schmid, U., Veith, H., Widder, J.: Tutorial on parameterized model checking of fault-tolerant distributed algorithms. In: Bernardo, M., Damiani, F., Hähnle, R., Johnsen, E.B., Schaefer, I. (eds.) SFM 2014. LNCS, vol. 8483, pp. 122–171. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  14. 14.
    Godefroid, P.: Using partial orders to improve automatic verification methods. In: Clarke, E., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 176–185. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  15. 15.
    Guerraoui, R.: Non-blocking atomic commit in asynchronous distributed systems with failure detectors. Distributed Computing 15(1), 17–25 (2002)CrossRefGoogle Scholar
  16. 16.
    John, A., Konnov, I., Schmid, U., Veith, H., Widder, J.: Parameterized model checking of fault-tolerant distributed algorithms by abstraction. In: FMCAD, pp. 201–209 (2013)Google Scholar
  17. 17.
    John, A., Konnov, I., Schmid, U., Veith, H., Widder, J.: Towards modeling and model checking fault-tolerant distributed algorithms. In: Bartocci, E., Ramakrishnan, C.R. (eds.) SPIN 2013. LNCS, vol. 7976, pp. 209–226. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  18. 18.
    Kroening, D., Ouaknine, J., Strichman, O., Wahl, T., Worrell, J.: Linear completeness thresholds for bounded model checking. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 557–572. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  19. 19.
    Kroning, D., Strichman, O.: Efficient computation of recurrence diameters. In: Zuck, L.D., Attie, P.C., Cortesi, A., Mukhopadhyay, S. (eds.) VMCAI 2003. LNCS, vol. 2575, pp. 298–309. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  20. 20.
    Lamport, L.: Time, clocks, and the ordering of events in a distributed system. Commun. ACM 21(7), 558–565 (1978)CrossRefMATHGoogle Scholar
  21. 21.
    Lamport, L., Schneider, F.B.: Pretending atomicity. Tech. Rep. 44, SRC (1989)Google Scholar
  22. 22.
    Leroux, J., Sutre, G.: Flat counter automata almost everywhere! In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 489–503. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  23. 23.
    Lipton, R.J.: Reduction: A method of proving properties of parallel programs. Commun. ACM 18(12), 717–721 (1975)CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Lubachevsky, B.D.: An approach to automating the verification of compact parallel coordination programs. II. Tech. Rep. 64, New York University. Computer Science Department (1983)Google Scholar
  25. 25.
    Lubachevsky, B.D.: An approach to automating the verification of compact parallel coordination programs. I. Acta Informatica 21(2), 125–169 (1984)Google Scholar
  26. 26.
    Lynch, N.: Distributed Algorithms. Morgan Kaufman (1996)Google Scholar
  27. 27.
    Mostéfaoui, A., Mourgaya, E., Parvédy, P.R., Raynal, M.: Evaluating the condition-based approach to solve consensus. In: DSN, pp. 541–550 (2003)Google Scholar
  28. 28.
    Peled, D.: All from one, one for all: on model checking using representatives. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 409–423. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  29. 29.
    Pnueli, A., Xu, J., Zuck, L.D.: Liveness with (0,1, ∞ )- counter abstraction. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 107–122. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  30. 30.
    Raynal, M.: A case study of agreement problems in distributed systems: Non-blocking atomic commitment. In: HASE, pp. 209–214 (1997)Google Scholar
  31. 31.
    Srikanth, T., Toueg, S.: Simulating authenticated broadcasts to derive simple fault-tolerant algorithms. Dist. Comp. 2, 80–94 (1987)CrossRefGoogle Scholar
  32. 32.
    Valmari, A.: Stubborn sets for reduced state space generation. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 491–515. Springer, Heidelberg (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Igor Konnov
    • 1
  • Helmut Veith
    • 1
  • Josef Widder
    • 1
  1. 1.Vienna University of Technology (TU Wien)WienAustria

Personalised recommendations