Comparison of the expressiveness of timed automata and time petri nets

  • Authors:

  • Beatrice Bérard;Franck Cassez;Serge Haddad;Didier Lime;Olivier H. Roux

  • Affiliations:

  • LAMSADE, Paris, France;IRCCyN, Nantes, France;LAMSADE, Paris, France;CISS, Aalborg, Denmark;IRCCyN, Nantes, France

  • Venue:
  • FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
  • Year:
  • 2005

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Abstract

In this paper we consider the model of Time Petri Nets (TPN) where time is associated with transitions. We also consider Timed Automata (TA) as defined by Alur & Dill, and compare the expressiveness of the two models w.r.t. timed language acceptance and (weak) timed bisimilarity. We first prove that there exists a TA $\mathcal{A}$s.t. there is no TPN (even unbounded) that is (weakly) timed bisimilar to $\mathcal{A}$. We then propose a structural translation from TA to (1-safe) TPNs preserving timed language acceptance. Further on, we prove that the previous (slightly extended) translation also preserves weak timed bisimilarity for a syntactical subclass $\mathcal{T}_{syn}(\leq,\geq)$of TA. For the theory of TPNs, the consequences are: 1) TA, bounded TPNs and 1-safe TPNs are equally expressive w.r.t. timed language acceptance; 2) TA are strictly more expressive than bounded TPNs w.r.t. timed bisimilarity; 3) The subclass $\mathcal{T}_{syn}(\leq,\geq)$, bounded and 1-safe TPNs “à la Merlin” are equally expressive w.r.t. timed bisimilarity.