On the Efficient Computation of the Minimal Coverability Set for Petri Nets

  • Gilles Geeraerts
  • Jean-François Raskin
  • Laurent Van Begin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4762)

Abstract

The minimal coverability set (MCS) of a Petri net is a finite representation of the downward-closure of its reachable markings. The minimal coverability set allows to decide several important problems like coverability, semi-liveness, place boundedness, etc. The classical algorithm to compute the MCS constructs the Karp&Miller tree [8]. Unfortunately the K&M tree is often huge, even for small nets. An improvement of this K&M algorithm is the Minimal Coverability Tree (MCT) algorithm [1], which has been introduced 15 years ago, and implemented since then in several tools such as Pep [7]. Unfortunately, we show in this paper that the MCT is flawed: it might compute an under-approximation of the reachable markings. We propose a new solution for the efficient computation of the MCS of Petri nets. Our experimental results show that this new algorithm behaves much better in practice than the K&M algorithm.

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References

  1. 1.
    Finkel, A.: The minimal coverability graph for Petri nets. In: Rozenberg, G. (ed.) Advances in Petri Nets 1993. LNCS, vol. 674, pp. 210–243. Springer, Heidelberg (1993)Google Scholar
  2. 2.
    Finkel, A., Geeraerts, G., Raskin, J.F., Van Begin, L.: A counter-example to the minimal coverability tree algorithm. Technical Report 535, Université Libre de Bruxelles (2005)Google Scholar
  3. 3.
    Geeraerts, G.: Coverability and Expressiveness Properties of Well-structured Transition Systems. PhD thesis, Université Libre de Bruxelles, Belgium (2007)Google Scholar
  4. 4.
    Geeraerts, G., Raskin, J.F., Van Begin, L.: Well-structured languages. Act. Inf. 44(3-4)Google Scholar
  5. 5.
    Geeraerts, G., Raskin, J.F., Van Begin, L.: On the efficient computation of the minimal coverability set for Petri nets. Technical Report CFV 2007.81Google Scholar
  6. 6.
    German, S., Sistla, A.: Reasoning about Systems with Many Processes. J. ACM 39(3) (1992)Google Scholar
  7. 7.
    Grahlmann, B.: The PEP tool. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 440–443. Springer, Heidelberg (1997)Google Scholar
  8. 8.
    Karp, R.M., Miller, R.E.: Parallel Program Schemata. JCSS 3, 147–195 (1969)MATHMathSciNetGoogle Scholar
  9. 9.
    Luttge, K.: Zustandsgraphen von Petri-Netzen. Master’s thesis, Humboldt-Universität (1995)Google Scholar
  10. 10.
    Reisig, W.: Petri Nets. An introduction. Springer, Heidelberg (1986)Google Scholar
  11. 11.
    Starke, P.: Personal communicationGoogle Scholar
  12. 12.
    Van Begin, L.: Efficient Verification of Counting Abstractions for Parametric systems. PhD thesis, Université Libre de Bruxelles, Belgium (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Gilles Geeraerts
    • 1
  • Jean-François Raskin
    • 1
  • Laurent Van Begin
    • 1
  1. 1.Université Libre de Bruxelles (U.L.B.), Computer Science Department, CPI 212, Campus Plaine, Boulevard du Triomphe, B-1050 BruxellesBelgium

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