CAV 2013: Computer Aided Verification pp 158-173 | Cite as

Incremental, Inductive Coverability

  • Johannes Kloos
  • Rupak Majumdar
  • Filip Niksic
  • Ruzica Piskac
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8044)

Abstract

We give an incremental, inductive (IC3) procedure to check coverability of well-structured transition systems. Our procedure generalizes the IC3 procedure for safety verification that has been successfully applied in finite-state hardware verification to infinite-state well-structured transition systems. We show that our procedure is sound, complete, and terminating for downward-finite well-structured transition systems —where each state has a finite number of states below it— a class that contains extensions of Petri nets, broadcast protocols, and lossy channel systems.

We have implemented our algorithm for checking coverability of Petri nets. We describe how the algorithm can be efficiently implemented without the use of SMT solvers. Our experiments on standard Petri net benchmarks show that IC3 is competitive with state-of-the-art implementations for coverability based on symbolic backward analysis or expand-enlarge-and-check algorithms both in time and space usage.

Keywords

Model Check Global State Coverability Problem Priority Queue Broadcast Protocol 
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.
    Abdulla, P.A., Cerans, K., Jonsson, B., Tsay, Y.-K.: General decidability theorems for infinite-state systems. In: LICS 1996, pp. 313–321. IEEE (1996)Google Scholar
  2. 2.
    Abdulla, P.A., Bouajjani, A., Jonsson, B.: On-the-fly analysis of systems with unbounded, lossy FIFO channels. In: Vardi, M.Y. (ed.) CAV 1998. LNCS, vol. 1427, pp. 305–318. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  3. 3.
    Bradley, A.R.: SAT-based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Ciardo, G.: Petri nets with marking-dependent arc multiplicity: properties and analysis. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 179–198. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  5. 5.
    Cimatti, A., Griggio, A.: Software model checking via IC3. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 277–293. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  6. 6.
    Dickson, L.E.: Finiteness of the odd perfect and primitive abundant numbers with n distinct prime factors. American Journal of Mathematics 35(4), 413–422 (1913)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Dufourd, C., Finkel, A., Schnoebelen, P.: Reset nets between decidability and undecidability. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 103–115. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  8. 8.
    Een, N., Mishchenko, A., Brayton, R.: Efficient implementation of property directed reachability. In: FMCAD 2011, pp. 125–134. FMCAD Inc. (2011)Google Scholar
  9. 9.
    Emerson, E.A., Namjoshi, K.S.: On model checking for non-deterministic infinite-state systems. In: LICS 1998, pp. 70–80. IEEE (1998)Google Scholar
  10. 10.
    Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: LICS 1999, pp. 352–359. IEEE Computer Society (1999)Google Scholar
  11. 11.
    Esparza, J., Nielsen, M.: Decidability issues for Petri nets – a survey. Bulletin of the EATCS 52, 244–262 (1994)Google Scholar
  12. 12.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comput. Sci. 256(1-2), 63–92 (2001)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Geeraerts, G., Raskin, J.-F., Van Begin, L.: Expand, enlarge and check: New algorithms for the coverability problem of WSTS. J. Comput. Syst. Sci. 72(1), 180–203 (2006)CrossRefMATHGoogle Scholar
  14. 14.
    Higman, G.: Ordering by divisibility in abstract algebras. Proceedings of the London Mathematical Society S3-2(1), 326–336 (1952)Google Scholar
  15. 15.
    Hoder, K., Bjørner, N.: Generalized property directed reachability. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 157–171. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  16. 16.
    Kaiser, A., Kroening, D., Wahl, T.: Efficient coverability analysis by proof minimization. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 500–515. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Kloos, J., Majumdar, R., Niksic, F., Piskac, R.: Incremental, inductive coverability. Technical Report 1301.7321, CoRR (2013)Google Scholar
  18. 18.
    Majumdar, R., Meyer, R., Wang, Z.: Static provenance verification for message-passing programs. In: SAS 2013 (2013)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Johannes Kloos
    • 1
    • 2
  • Rupak Majumdar
    • 1
    • 2
  • Filip Niksic
    • 1
    • 2
  • Ruzica Piskac
    • 1
    • 2
  1. 1.MPI-SWSKaiserslauternGermany
  2. 2.MPI-SWSSaarbrückenGermany

Personalised recommendations