Attacking the Dimensionality Problem of Parameterized Systems via Bounded Reachability Graphs

  • Qiusong Yang
  • Bei Zhang
  • Jian Zhai
  • Mingshu Li
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7141)

Abstract

Parameterized systems are systems that involve numerous instantiations of finite-state processes, and depend on parameters which define their size. The verification of parameterized systems is to decide if a property holds in its every size instance, essentially a problem with an infinite state space, and thus poses a great challenge to the community. Starting with a set of undesired states represented by an upward-closed set, the backward reachability analysis will always terminate because of the well-quasi-orderingness. As a result, backward reachability analysis has been widely used in the verification of parameterized systems. However, many existing approaches are facing with the dimensionality problem, which describes the phenomenon that the memory used for storing the symbolic state space grows extremely fast when the number of states of the finite-state process increases, making the verification rather inefficient. Based on bounded backward reachability graphs, a novel abstraction for parameterized systems, we have developed an approach for building abstractions with incrementally increased dimensions and thus improving the precision until a property is proven or a counterexample is detected. The experiments show that the verification efficiencies have been significantly improved because conclusive results tend to be drawn on abstractions with much lower dimensions.

Keywords

Parameterized System Model Check Dimensionality Problem User Process Reachability Analysis 
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.
    Zuck, L.D., Pnueli, A.: Model checking and abstraction to the aid of parameterized systems (a survey). Computer Languages, Systems & Structures 30(3-4), 139–169 (2004)MATHCrossRefGoogle Scholar
  2. 2.
    Apt, K.R., Kozen, D.C.: Limits for automatic verification of finite-state concurrent systems. Inf. Process. Lett. 22(6), 307–309 (1986)MathSciNetCrossRefGoogle Scholar
  3. 3.
    German, S.M., Sistla, A.P.: Reasoning about systems with many processes. J. ACM 39(3), 675–735 (1992)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Emerson, E.A., Namjoshi, K.S.: On model checking for non-deterministic infinite-state systems. In: Logic in Computer Science, pp. 70–80 (1998)Google Scholar
  5. 5.
    Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: LICS 1999: Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science, p. 352. IEEE Computer Society, Washington, DC (1999)Google Scholar
  6. 6.
    Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.K.: General decidability theorems for infinite-state systems. In: LICS 1996: Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science, pp. 313–321. IEEE Computer Society, Washington, DC (1996)CrossRefGoogle Scholar
  7. 7.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere? Theor. Comput. Sci. 256(1-2), 63–92 (2001)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Delzanno, G.: Constraint-Based Model Checking for Parameterized Synchronous Systems. In: Armando, A. (ed.) FroCos 2002. LNCS (LNAI), vol. 2309, pp. 72–318. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Delzanno, G., Raskin, J.-F., Van Begin, L.: Attacking Symbolic State Explosion. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 298–310. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  10. 10.
    Delzanno, G., Raskin, J.-F.: Symbolic Representation of Upward-Closed Sets. In: Graf, S. (ed.) TACAS 2000. LNCS, vol. 1785, pp. 426–440. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  11. 11.
    Delzanno, G., Esparza, J., Podelski, A.: Constraint-Based Analysis of Broadcast Protocols. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 50–66. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  12. 12.
    Esparza, J.: Verification of Systems with an Infinite State Space. In: Cassez, F., Jard, C., Rozoy, B., Dermot, M. (eds.) MOVEP 2000. LNCS, vol. 2067, pp. 183–186. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification (preliminary report). In: Meyer, A. (ed.) Proceedings of the First Annual IEEE Symp. on Logic in Computer Science, LICS 1986, pp. 332–344. IEEE Computer Society Press (1986)Google Scholar
  14. 14.
    Dwyer, M.B., Clarke, L.A., Cobleigh, J.M., Naumovich, G.: Flow analysis for verifying properties of concurrent software systems. ACM Trans. Softw. Eng. Methodol. 13(4), 359–430 (2004)CrossRefGoogle Scholar
  15. 15.
    Delzanno, G.: Constraint-based verification of parameterized cache coherence protocols. Form. Methods Syst. Des. 23(3), 257–301 (2003)MATHCrossRefGoogle Scholar
  16. 16.
    Dwyer, M.B., Person, S., Elbaum, S.G.: Controlling factors in evaluating path-sensitive error detection techniques. In: Young, M., Devanbu, P.T. (eds.) SIGSOFT FSE, pp. 92–104. ACM (2006)Google Scholar
  17. 17.
    Bingham, J.D.: A new approach to upward-closed set backward reachability analysis. Electr. Notes Theor. Comput. Sci. 138(3), 37–48 (2005)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Yang, Q., Li, M.: A cut-off approach for bounded verification of parameterized systems. In: Proceedings of the 32nd ACM/IEEE International Conference on Software Engineering, ICSE 2010, vol. 1, pp. 345–354. ACM, New York (2010)CrossRefGoogle Scholar
  19. 19.
    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

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Qiusong Yang
    • 1
  • Bei Zhang
    • 1
    • 3
  • Jian Zhai
    • 1
  • Mingshu Li
    • 1
    • 2
  1. 1.National Engineering Research Center of Fundamental Software, Institute of SoftwareChinese Academy of SciencesBeijingChina
  2. 2.State Key Laboratory of Computer Science, Institute of SoftwareChinese Academy of SciencesBeijingChina
  3. 3.Graduate University of Chinese Academy of SciencesBeijingChina

Personalised recommendations