Complexity analysis of continuous Petri nets

Abstract

At the end of the eighties, continuous Petri nets were introduced for: (1) alleviating the combinatory explosion triggered by discrete Petri nets and, (2) modelling the behaviour of physical systems whose state is composed of continuous variables. Since then several works have established that the computational complexity of deciding some standard behavioural properties of Petri nets is reduced in this framework. Here we first establish the decidability of additional properties like boundedness and reachability set inclusion. We also design new decision procedures for the reachability and lim-reachability problems with a better computational complexity. Finally we provide lower bounds characterising the exact complexity class of the boundedness, the reachability, the deadlock freeness and the liveness problems. © 2013 Springer-Verlag.