On the Efficient Computation of the Minimal Coverability Set for Petri Nets
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 . 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 , which has been introduced 15 years ago, and implemented since then in several tools such as Pep . 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.
KeywordsCovering Sequence Monotonicity Property Recursive Call Label Tree Strict Monotonicity
Unable to display preview. Download preview PDF.
- 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.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.Geeraerts, G.: Coverability and Expressiveness Properties of Well-structured Transition Systems. PhD thesis, Université Libre de Bruxelles, Belgium (2007)Google Scholar
- 4.Geeraerts, G., Raskin, J.F., Van Begin, L.: Well-structured languages. Act. Inf. 44(3-4)Google Scholar
- 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.German, S., Sistla, A.: Reasoning about Systems with Many Processes. J. ACM 39(3) (1992)Google Scholar
- 7.Grahlmann, B.: The PEP tool. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 440–443. Springer, Heidelberg (1997)Google Scholar
- 9.Luttge, K.: Zustandsgraphen von Petri-Netzen. Master’s thesis, Humboldt-Universität (1995)Google Scholar
- 10.Reisig, W.: Petri Nets. An introduction. Springer, Heidelberg (1986)Google Scholar
- 11.Starke, P.: Personal communicationGoogle Scholar
- 12.Van Begin, L.: Efficient Verification of Counting Abstractions for Parametric systems. PhD thesis, Université Libre de Bruxelles, Belgium (2003)Google Scholar