ON THE EFFICIENT COMPUTATION OF THE MINIMAL COVERABILITY SET OF PETRI NETS

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 (KM) tree [10]. Unfortunately the KM tree is often huge, even for small nets. An improvement of this KM algorithm is the Minimal Coverability Tree (MCT) algorithm [3], which has been introduced nearly 20 years ago, and implemented since then in several tools such as Pep [9]. 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 algorithm is based on new ideas, and the experimental results show that it behaves much better in practice than the KM algorithm.