Optimisation de la construction d'une approximation de l'espace d'état des systèmes préemptifs

We present in this paper an algorithm allowing an efficient computation of the tightest DBM over-approximation of the state class graph of preemptive systems modeled by using Time Petri Nets with inhibitor arcs. For this effect, we express each class of the approximated graph as a pair (M, D), where M is a marking and D is the system of all DBM inequalities even the redundant ones. We thereby make it possible to compute the system D straightforwardly in its normal form, without requiring to compute the intermediary polyhedra. Hence, we succeed to reduce appreciably the computation cost of a class, and to remove the implementation dysfunctions reported for other approaches. We also discuss how to determine from the graph linear and quantitative properties of the model. Finally, we give some experimental results that compare the implementations of the different approaches.