Decidability results in First–Order Hybrid PetriNets

  • Authors:

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

  • Affiliations:

  • Dip. di Automatica ed Informatica, Politecnico di Torino, Italy;Dip. di Automatica ed Informatica, Politecnico di Torino, Italy;Dip. di Ingegneria Elettrica ed Elettronica, Università di Cagliari, Italy;Dip. di Ingegneria Elettrica ed Elettronica, Università di Cagliari, Italy

  • Venue:
  • Discrete Event Dynamic Systems
  • Year:
  • 2001

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Abstract

In this paper we tackle the decidabilityof marking reachability for a hybrid formalism based on Petrinets. The model we consider is the untimed version of First–OrderHybrid Petri Nets: it combines a discrete Petri net and a continuousPetri net, the latter being a fluid version of a usual discretePetri net. It is suggested that the decidability results shouldbe pursued exploiting a hierarchy of models as it has been donein the framework of Hybrid Automata. In this paper we definethe class of Single–Rate Hybrid Petri Nets: the continuousdynamics of these nets is such that the vector of the markingderivatives of the continuous places is constant but for a scalarfactor. This class of nets can be seen as the counterpart oftimed automata with skewed clocks. We prove that the reachabilityproblem for this class can be reduced to the reachability problemof an equivalent discrete net and thus it is decidable.