On the computation of the minimal coverability set of Petri nets
Résumé
The verification of infinite-state systems is a challenging task. A prominent instance is reachability analysis of Petri nets, for which no efficient algorithm is known. The minimal coverability set of a Petri net can be understood as an approximation of its reachability set described by means of ω -markings (i.e. markings in which some entries may be set to infinity). It allows to solve numerous decision problems on Petri nets, such as any coverability problem. In this paper, we study the computation of the minimal coverability set.
This set can be computed using the Karp and Miller trees, which perform accelerations of cycles along branches [10]. The resulting algorithm may however perform redundant computations. In a previous work [17], we proposed an improved algorithm allowing pruning between branches of the Karp and Miller tree, and proved its correctness. The proof of its correctness was complicated, as the introduction of pruning between branches may yield to incompleteness issues [5, 9].
In this paper, we propose a new proof of the correctness of our algorithm. This new proof relies on an original invariant of the algorithm, leading to the following assets:
1. it is considerably shorter and simpler,
2. it allows to prove the correctness of a more generic algorithm, as the acceleration used is let as a parameter. Indeed, we identify the property that the acceleration should satisfy to ensure completeness.
3. it opens the way to a generalization of our algorithm to extensions of Petri nets.
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