Comparison of the Expressiveness of Timed Automata and Time Petri Nets

Béatrice Berard (1, 2) , Franck Cassez (3, 4) , Serge Haddad (2, 5) , Didier Lime (3) , Olivier Henri Roux (3)

1 MoVe - Modélisation et Vérification
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
3 IRCCyN - Institut de Recherche en Communications et en Cybernétique de Nantes
4 NICTA - National ICT Australia [Sydney]
5 LSV - Laboratoire Spécification et Vérification [Cachan]

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 expressive- ness of the two models w.r.t. timed language acceptance and (weak) timed bisimilarity. We first prove that there exists a TA A s.t. there is no TPN (even unbounded) that is (weakly) timed bisimilar to A. We then propose a structural translation from TA to (1-safe) TPNs preserv- ing timed language acceptance. Further on, we prove that the previous (slightly extended) translation also preserves weak timed bisimilarity for a syntactical subclass $T_{Asyn}(\leq,\geq)$ 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 $T_{Asyn}(\leq,\geq)$, bounded and 1-safe TPNs ''`a la Merlin'' are equally ex- pressive w.r.t. timed bisimilarity.

Domaines: Logique en informatique [cs.LO]

Béatrice Berard, Franck Cassez, Serge Haddad, Didier Lime, Olivier Henri Roux. Comparison of the Expressiveness of Timed Automata and Time Petri Nets. FORMATS 2005 - 3rd International Conference on Formal Modeling and Analysis of Timed Systems, Sep 2005, Uppsala, Sweden. pp.211-225, ⟨10.1007/11603009_17⟩. ⟨inria-00368577⟩