Linear algebraic calculation of deadlocks and traps
Concurrency and nets: advances in Petri nets
Selected papers on First international colloquium on pseudo-boolean optimization and related topics
Petri Net Theory and the Modeling of Systems
Petri Net Theory and the Modeling of Systems
Petri Net Representations in Metabolic Pathways
Proceedings of the 1st International Conference on Intelligent Systems for Molecular Biology
Modeling and querying biomolecular interaction networks
Theoretical Computer Science - Special issue: Computational systems biology
Petri nets for systems and synthetic biology
SFM'08 Proceedings of the Formal methods for the design of computer, communication, and software systems 8th international conference on Formal methods for computational systems biology
Hard and easy distributions of SAT problems
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
Experimental results on the crossover point in satisfiability problems
AAAI'93 Proceedings of the eleventh national conference on Artificial intelligence
Petriweb: a repository for petri nets
ICATPN'06 Proceedings of the 27th international conference on Applications and Theory of Petri Nets and Other Models of Concurrency
Enumeration algorithms for minimal siphons in Petri nets based on place constraints
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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Petri nets are a simple formalism for modeling concurrent computation. Recently, they have emerged as a promising tool for modeling and analyzing biochemical interaction networks, bridging the gap between purely qualitative and quantitative models. Biological networks can indeed be large and complex, which makes their study difficult and computationally challenging. In this paper, we focus on two structural properties of Petri nets, siphons and traps, that bring us information about the persistence of some molecular species. We present two methods for enumerating all minimal siphons and traps of a Petri net by iterating the resolution of Boolean satisfiability problems executed with either a SAT solver or a CLP(B) program. We compare the performances of these methods with respect to a state-of-the-art algorithm from the Petri net community. On a benchmark with 80 Petri nets from the Petriweb database and 403 Petri nets from curated biological models of the Biomodels database, we show that miniSAT and CLP(B) solvers are overall both faster by two orders of magnitude with respect to the dedicated algorithm. Furthermore, we analyse why these programs perform so well on even very large biological models and show the existence of hard instances in Petri nets with unbounded degrees.