When are Timed Automata weakly timed bisimilar to Time Petri Nets?

In this paper, we compare Timed Automata (TA) and Time Petri Nets (TPN) with respect to weak timed bisimilarity. It is already known that the class of bounded TPNs is strictly included in the class of TA. It is thus natural to try and identify the subclass TAwtb of TA equivalent to some TPN for the weak timed bisimulation relation. We give a characterization of this subclass and we show that the membership problem and the reachability problem for TAwtb are PSPACE-complete. Furthermore we show that for a TA in TAwtb with integer constants, an equivalent TPN can be built with integer bounds but with a size exponential w.r.t. the original model. Surprisingly, using rational bounds yields a TPN whose size is linear.