Comparison of the Expressiveness of Timed Automata and Time Petri Nets

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 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.