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 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.KeywordsTimed LanguageTimed BisimilarityTime Petri NetsTimed AutomataExpressiveness