On enumerating minimal siphons in Petri nets using CLP and SAT solvers: theoretical and practical complexity

Abstract Petri nets are a simple formalism for modeling concurrent computation. They are also an interesting tool for modeling and analysing biochemical reaction systems, bridging the gap between purely qualitative and quantitative models. Biological networks can indeed be complex, large, and with many unknown kinetic parameters, which makes the development of quantitative models difficult. In this paper, we focus on the Petri net representation of biochemical reactions and on two structural properties of Petri nets, siphons and traps, that bring us information about the persistence of some molecular species, independently of the kinetics. We first study the theoretical time complexity of minimal siphon decision problems in general Petri nets, and present three new complexity results: first, we show that the existence of a siphon of a given cardinality is NP-complete; second, we prove that deciding the SiphonTrap property is co-NP-complete; third, we prove that deciding the existence...

• Type: Journal
• Year: 2016
• Where: CONSTRAINTS
• Authors: Faten Nabli, Thierry Martinez, François Fages, Sylvain Soliman
• Keywords: CONSTRAINTS 2016