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.
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Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H. (2005). Comparison of the Expressiveness of Timed Automata and Time Petri Nets. In: Pettersson, P., Yi, W. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2005. Lecture Notes in Computer Science, vol 3829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11603009_17
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