Advertisement

All for the Price of Few

(Parameterized Verification through View Abstraction)
  • Parosh Aziz Abdulla
  • Frédéric Haziza
  • Lukáš Holík
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7737)

Abstract

We present a simple and efficient framework for automatic verification of systems with a parameteric number of communicating processes. The processes may be organized in various topologies such as words, multisets, rings, or trees. Our method needs to inspect only a small number of processes in order to show correctness of the whole system. It relies on an abstraction function that views the system from the perspective of a fixed number of processes. The abstraction is used during the verification procedure in order to dynamically detect cut-off points beyond which the search of the state space need not continue. We show that the method is complete for a large class of well quasi-ordered systems including Petri nets. Our experimentation on a variety of benchmarks demonstrate that the method is highly efficient and that it works well even for classes of systems with undecidable verification problems.

Keywords

Model Check Transition Rule Ring Topology Reachability Analysis Tree Automaton 
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.
    Abdulla, P.A.: Well (and better) quasi-ordered transition systems. Bulletin of Symbolic Logic 16(4), 457–515 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Abdulla, P.A., Čerāns, K., Jonsson, B., Tsay, Y.K.: General decidability theorems for infinite-state systems. In: LICS 1996, pp. 313–321 (1996)Google Scholar
  3. 3.
    Abdulla, P.A., Delzanno, G., Ben Henda, N., Rezine, A.: Regular Model Checking Without Transducers (On Efficient Verification of Parameterized Systems). In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 721–736. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Abdulla, P.A., Ben Henda, N., Delzanno, G., Rezine, A.: Handling Parameterized Systems with Non-atomic Global Conditions. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 22–36. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Abdulla, P.A., Jonsson, B., Nilsson, M., d’Orso, J.: Regular Model Checking Made Simple and Efficient. In: Brim, L., Jančar, P., Křetínský, M., Kučera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, pp. 116–130. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Arons, T., Pnueli, A., Ruah, S., Xu, J., Zuck, L.: Parameterized Verification with Automatically Computed Inductive Assertions. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 221–234. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Baukus, K., Lakhnech, Y., Stahl, K.: Parameterized Verification of a Cache Coherence Protocol: Safety and Liveness. In: Cortesi, A. (ed.) VMCAI 2002. LNCS, vol. 2294, pp. 317–330. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  8. 8.
    Bingham, J.D., Hu, A.J.: Empirically Efficient Verification for a Class of Infinite-State Systems. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 77–92. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Boigelot, B., Legay, A., Wolper, P.: Iterating Transducers in the Large. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 223–235. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Bouajjani, A., Habermehl, P., Vojnar, T.: Abstract Regular Model Checking. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 372–386. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Clarke, E., Talupur, M., Veith, H.: Environment Abstraction for Parameterized Verification. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 126–141. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  12. 12.
    Dams, D., Lakhnech, Y., Steffen, M.: Iterating Transducers. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 286–297. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Delzanno, G.: Automatic Verification of Cache Coherence Protocols. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 53–68. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Delzanno, G.: Verification of consistency protocols via infinite-state symbolic model checking. In: FORTE 2000. IFIP Conference Proceedings, vol. 183, pp. 171–186. Kluwer (2000)Google Scholar
  15. 15.
    Emerson, E.A., Kahlon, V.: Reducing Model Checking of the Many to the Few. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 236–254. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  16. 16.
    Emerson, E.A., Namjoshi, K.: Reasoning about rings. In: POPL 1995, pp. 85–94 (1995)Google Scholar
  17. 17.
    Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: LICS 1999. IEEE Computer Society (1999)Google Scholar
  18. 18.
    Flanagan, C., Qadeer, S.: Thread-Modular Model Checking. In: Ball, T., Rajamani, S.K. (eds.) SPIN 2003. LNCS, vol. 2648, pp. 213–224. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Ganty, P., Raskin, J.-F., Van Begin, L.: A Complete Abstract Interpretation Framework for Coverability Properties of WSTS. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 49–64. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Geeraerts, G., Raskin, J.-F., Van Begin, L.: Expand, Enlarge and Check.. Made Efficient. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 394–407. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. 21.
    Geeraerts, G., Raskin, J.F., Begin, L.V.: Expand, Enlarge and Check: New algorithms for the coverability problem of WSTS. J. Comput. Syst. Sci. 72(1), 180–203 (2006)zbMATHCrossRefGoogle Scholar
  22. 22.
    German, S.M., Sistla, A.P.: Reasoning about systems with many processes. J. ACM 39(3), 675–735 (1992)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Holzmann, G.J.: The model checker spin. IEEE Trans. Software Eng. 23(5), 279–295 (1997)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Kaiser, A., Kroening, D., Wahl, T.: Dynamic Cutoff Detection in Parameterized Concurrent Programs. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 645–659. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  25. 25.
    Kesten, Y., Maler, O., Marcus, M., Pnueli, A., Shahar, E.: Symbolic model checking with rich assertional languages. Theor. Comput. Sci. 256, 93–112 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    Lynch, N.A., Shamir, B.P.: Distributed algorithms, lecture notes for 6.852, fall 1992. Tech. Rep. MIT/LCS/RSS-20, MIT (1993)Google Scholar
  27. 27.
    Malkis, A., Podelski, A., Rybalchenko, A.: Thread-Modular Verification Is Cartesian Abstract Interpretation. In: Barkaoui, K., Cavalcanti, A., Cerone, A. (eds.) ICTAC 2006. LNCS, vol. 4281, pp. 183–197. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  28. 28.
    Malkis, A., Podelski, A., Rybalchenko, A.: Precise Thread-Modular Verification. In: Riis Nielson, H., Filé, G. (eds.) SAS 2007. LNCS, vol. 4634, pp. 218–232. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  29. 29.
    Namjoshi, K.S.: Symmetry and Completeness in the Analysis of Parameterized Systems. In: Cook, B., Podelski, A. (eds.) VMCAI 2007. LNCS, vol. 4349, pp. 299–313. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  30. 30.
    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
  31. 31.
    Pnueli, A., Ruah, S., Zuck, L.D.: Automatic Deductive Verification with Invisible Invariants. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 82–97. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  32. 32.
    Touili, T.: Regular Model Checking using Widening Techniques. Electronic Notes in Theoretical Computer Science 50(4) (2001); Proc. of VEPAS 2001Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Parosh Aziz Abdulla
    • 1
  • Frédéric Haziza
    • 1
  • Lukáš Holík
    • 1
    • 2
  1. 1.Uppsala UniversitySweden
  2. 2.Brno University of TechnologyCzech Republic

Personalised recommendations