Decidability results in firstorder hybrid petri nets. Discrete Event Dynamic Systems

In this paper we tackle the decidability of marking reachability for a hybrid formalism based on Petri nets. The model we consider is the untimed version of First–Order Hybrid Petri Nets: it combines a discrete Petri net and a continuous Petri net, the latter being a fluid version of a usual discrete Petri net. It is suggested that the decidability results should be pursued exploiting a hierarchy of models as it has been done in the framework of Hybrid Automata. In this paper we define the class of Single–Rate Hybrid Petri Nets: the continuous dynamics of these nets is such that the vector of the marking derivatives of the continuous places is constant but for a scalar factor. This class of nets can be seen as the counterpart of timed automata with skewed clocks. We prove that the reachability problem for this class can be reduced to the reachability problem of an equivalent discrete net and thus it is decidable.