When Are Timed Automata Weakly Timed Bisimilar to Time Petri Nets?

Abstract

In this paper, we compare Timed Automata (TA) with Time Petri Nets (TPN) with respect to weak timed bisimilarity. It is already known that the class of bounded TPNs is included in the class of TA. It is thus natural to try and identify the (strict) subclass ${\cal TA}^{wtb}$ of TA that is equivalent to TPN for the weak time bisimulation relation. We give a characterisation of this subclass and we show that the membership problem and the reachability problem for ${\cal TA}^{wtb}$ are PSPACE-complete. Furthermore we show that for a TA in ${\cal TA}^{wtb}$ 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.