Abstract. In this paper, we present a general algorithmic schema called "Expand, Enlarge and Check" from which new efficient algorithms for the coverability problem of WSTS can be constructed. We show here that our schema allows us to define forward algorithms that decide the coverability problem for several classes of systems for which the Karp and Miller procedure cannot be generalized, and for which no complete forward algorithms were known. Our results have important applications for the verification of parameterized systems and communication protocols.

In this paper we investigate the possible application of parameterized verification techniques to synchronization skeletons of multithreaded Java programs. As conceptual contribution, we identify a class of infinite-state abstract models, called Multi-Transfer Nets (MTNs), that preserve the main features of the semantics of concurrent Java. We achieve this goal by exploiting an interesting connection with the Broadcast Protocols of [7], and by introducing the notion of asynchronous rendezvous. As technical contribution, we extend the symbolic verification techniques of [6] based on Covering Sharing Trees and structural invariants to MTNs. As practical contribution, we report on experimental results for verification of examples of multithreaded Java programs.

In this paper, we present a general algorithmic schema called 'Expand, Enlarge and Check' from which new algorithms for the coverability problem of WSTS can be constructed. We show here that our schema allows us to define forward algorithms that decide the coverability problem for several classes of systems for which the Karp and Miller procedure cannot be generalized, and for which no complete forward algorithms were known. Our results have important applications for the verification of parameterized systems and communication protocols.A preliminary version of this paper has been published as [Geeraerts et al., Expand, enlarge and check: new algorithms for the coverability problem of WSTS, in:

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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, semiliveness, place boundedness, etc. The classical algorithm to compute the MCS constructs the Karp&Miller tree [1]. 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 [2], which has been introduced 15 years ago, and implemented since then in several tools such as Pep [3]. 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.