Post and pre-initialized stopwatch Petri nets: Formal semantics and state space computation

We give the formal semantics of this model as a timed transitions system and we position SWPN with regard to other classes of Petri nets destined to model preemptive behavior. We also propose a method for computing the state space of a SWPN as a stopwatch automaton. The method consists of labeling firstly the marking graph of a SWPN as a stopwatch automaton. Then, a forward region-based algorithm is applied to this automaton by using an analyzing tool on linear hybrid system PHAVer in order to compute its reachable states. The obtained automaton is proved to be timed bisimilar to initial SWPN. Thus, the verification of quantitative properties can be conducted thanks to the such obtained automaton.