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Decidability results in first-order hybrid Petri nets.

Balduzzi, Fabio; Di Febbraro, Angela; Giua, Alessandro; Seatzu, Carla

In: Discrete Event Dynamic Systems:Theory and Applications, 11, pages 41-57. 2001.

Abstract: In this paper the decidability of marking reachability for a hybrid formalism based on Petri nets is tackled. As a model the untimed version of First-Order Hybrid Petri Nets is chosen: 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 the class of Single-Rate Hybrid Petri Nets is defined: 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. The reachability problem for this class is reduced to the reachability problem of an equivalent discrete net and thus decidable.

Keywords: Hybrid automata, timed automata, hybrid Petri nets, decidability properties.

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