Expressiveness and analysis of Delayable Timed Petri Net*

Abstract

We consider an extension of Timed Petri Nets “à la Ramchandani” where the transitions are partitioned into delayable and non-delayable transitions which has proven to be suitable for the design of synchronous circuits. For this model called Delayable Timed Petri Net (DTPN), the firing delay of a non-delayable transition is strict whereas a delayable transition can miss its firing delay. Since the delays are natural numbers, this model can be studied as a discrete time model.We deal with the expressiveness of DTPN by a comparison with the well known Merlin's Time Petri Net model for which transitions can fire in a time interval. We show that DTPN are strictly more expressive w.r.t. weak timed bisimilarity than Merlin's model under the discrete-time semantics. We then deal with the symbolic reachability analysis of DTPN, for which we show the complexity of the successor symbolic state computation to be O(n). In addition, we propose a reduction of the number of edges to explore that preserves the markings and the firing sequences. The symbolic state space exploration is implemented in a prototype tool, which is evaluated on a classical TPN problem and a circuit design application.