Comparison of the Expressiveness of Timed Automata and Time Petri Nets. Bérard, B., Cassez, F., Haddad, S., Lime, D., & Roux, O. H. In Pettersson, P. & Yi, W., editors, Formal Modeling and Analysis of Timed Systems, Third International Conference, FORMATS 2005, Uppsala, Sweden, September 26-28, 2005, Proceedings, volume 3829, of Lecture Notes in Computer Science, pages 211–225, 2005. Springer.
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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 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 preserving timed language acceptance. Further on, we prove that the previous (slightly extended) translation also preserves weak timed bisimilarity for a syntactical subclass 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 bounded and 1-safe TPNs “`a la Merlin” are equally expressive w.r.t. timed bisimilarity.

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