Verification of Petri Nets with Read Arcs

  • César Rodríguez
  • Stefan Schwoon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7454)

Abstract

Recent work studied the unfolding construction for contextual nets, i.e. nets with read arcs. Such unfoldings are more concise and can usually be constructed more efficiently than for Petri nets. However, concrete verification algorithms exploiting these advantages were lacking so far. We address this question and propose SAT-based verification algorithms for deadlock and reachability of contextual nets. Moreover, we study optimizations of the SAT encoding and report on experiments.

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References

  1. 1.
    Baldan, P., Bruni, A., Corradini, A., König, B., Schwoon, S.: On the Computation of McMillan’s Prefix for Contextual Nets and Graph Grammars. In: Ehrig, H., Rensink, A., Rozenberg, G., Schürr, A. (eds.) ICGT 2010. LNCS, vol. 6372, pp. 91–106. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Baldan, P., Corradini, A., König, B., Schwoon, S.: McMillan’s Complete Prefix for Contextual Nets. In: Jensen, K., van der Aalst, W.M.P., Billington, J. (eds.) ToPNoC 1. LNCS, vol. 5100, pp. 199–220. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Chen, J.: A new SAT encoding of the at-most-one constraint. In: Proc. Constraint Modelling and Reformulation (2010)Google Scholar
  4. 4.
    Codish, M., Genaim, S., Stuckey, P.J.: A declarative encoding of telecommunications feature subscription in SAT. In: Proc. PPDP, pp. 255–266. ACM (2009)Google Scholar
  5. 5.
    Diekert, V., Gastin, P.: From local to global temporal logics over Mazurkiewicz traces. Theoretical Computer Science 356(1-2), 126–135 (2006)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Eén, N., Sörensson, N.: An Extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Esparza, J., Heljanko, K.: Implementing LTL Model Checking with Net Unfoldings. In: Dwyer, M.B. (ed.) SPIN 2001. LNCS, vol. 2057, pp. 37–56. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Esparza, J., Heljanko, K.: Unfoldings - A Partial-Order Approach to Model Checking. EATCS Monographs in Theoretical Computer Science. Springer (2008)Google Scholar
  9. 9.
    Esparza, J., Römer, S., Vogler, W.: An improvement of McMillan’s unfolding algorithm. Formal Methods in System Design 20, 285–310 (2002)MATHCrossRefGoogle Scholar
  10. 10.
    Esparza, J., Schröter, C.: Unfolding based algorithms for the reachability problem. Fund. Inf. 47(3-4), 231–245 (2001)MATHGoogle Scholar
  11. 11.
    Heljanko, K.: Using logic programs with stable model semantics to solve deadlock and reachability problems for 1-safe Petri nets. Fund. Inf. 37(3), 247–268 (1999)MathSciNetMATHGoogle Scholar
  12. 12.
    Khomenko, V.: Model Checking Based on Prefixes of Petri Net Unfoldings. Ph.D. thesis, School of Computing Science, Newcastle University (2003)Google Scholar
  13. 13.
    Khomenko, V., Kondratyev, A., Koutny, M., Vogler, W.: Merged processes – a new condensed representation of Petri net behaviour. Act. Inf. 43(5), 307–330 (2006)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Khomenko, V., Koutny, M.: LP Deadlock Checking Using Partial Order Dependencies. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 410–425. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Khomenko, V., Koutny, M.: Verification of bounded Petri nets using integer programming. Formal Methods in System Design 30(2), 143–176 (2007)MATHCrossRefGoogle Scholar
  16. 16.
  17. 17.
    McMillan, K.L.: Using Unfoldings to avoid the State Explosion Problem in the Verification of Asynchronous Circuits. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 164–177. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  18. 18.
    Melzer, S., Römer, S.: Deadlock Checking using Net Unfoldings. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 352–363. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  19. 19.
    Raynal, M.: Algorithms for Mutual Exclusion. MIT Press (1986)Google Scholar
  20. 20.
  21. 21.
    Rodríguez, C., Schwoon, S.: Verification of Petri Nets with Read Arcs. Tech. Rep. LSV-12-12, LSV, ENS de Cachan (2012)Google Scholar
  22. 22.
    Rodríguez, C., Schwoon, S., Baldan, P.: Efficient Contextual Unfolding. In: Katoen, J.-P., König, B. (eds.) CONCUR 2011. LNCS, vol. 6901, pp. 342–357. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  23. 23.
    Schröter, C.: Halbordnungs- und Reduktionstechniken für die automatische Verifikation von verteilten Systemen. Ph.D. thesis, Universität Stuttgart (2006)Google Scholar
  24. 24.
  25. 25.
    Schwoon, S., Rodríguez, C.: Construction and SAT-Based Verification of Contextual Unfoldings. In: Holzer, M. (ed.) DCFS 2011. LNCS, vol. 6808, pp. 34–42. Springer, Heidelberg (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • César Rodríguez
    • 1
  • Stefan Schwoon
    • 1
  1. 1.LSV (ENS Cachan & CNRS & INRIA)France

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