On the Compared Expressiveness of Arc, Place and Transition Time Petri Nets

In this paper, we consider safe Time Petri Nets where time intervals (strict and large) are associated with places (P-TPN), arcs (A-TPN) or transitions (T-TPN). We give the formal strong and weak semantics of these models in terms of Timed Transition Systems. We compare the expressiveness of the six models w.r.t. (weak) timed bisimilarity (behavioral semantics). The main results of the paper are : (i) with strong semantics, A-TPN is strictly more expressive than P-TPN and T-TPN ; (ii) with strong semantics P-TPN and T-TPN are incomparable ; (iii) T-TPN with strong semantics and T-TPN with weak semantics are incomparable. Moreover, we give a complete classification by a set of 9 relations explained in Fig. 19 (p. 23).