On the efficient computation of the minimal coverability set for Petri nets

  • Authors:

  • Gilles Geeraerts;Jean-François Raskin;Laurent Van Begin

  • Affiliations:

  • Université Libre de Bruxelles, Computer Science Department, Boulevard du Triomphe, Bruxelles, Belgium;Université Libre de Bruxelles, Computer Science Department, Boulevard du Triomphe, Bruxelles, Belgium;FNRS, Belgium and Université Libre de Bruxelles, Computer Science Department, Boulevard du Triomphe, Bruxelles, Belgium

  • Venue:
  • ATVA'07 Proceedings of the 5th international conference on Automated technology for verification and analysis
  • Year:
  • 2007

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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.