Decidability, expressivity and state-space computation of stopwatch Petri nets with discrete-time semantics

Abstract

In this paper, we address the general class of bounded Petri nets with stopwatches (SwPNs), which is an extension of T-time Petri nets (TPNs) where time is associated with transitions. Stopwatches can be reset, stopped and started. Our goal is to apply a discrete approach: we propose a structural translation from this model to classical Petri nets with flush arcs and inhibitor hyperarcs. Further on, we prove that this translation preserves weak timed bisimilarity. For the theory of Petri nets with stopwatches, the consequences are both theoretical and practical: 1) Petri nets with flush arcs and inhibitor hyperarcs, discrete-time TPNs and 1-safe discrete-time SwTPNs are equally expressive w.r.t. timed bisimilarity, thus timed language acceptance; 2) reachability problem - undecidable with dense-time semantics - becomes decidable once discrete-time is considered; 3) state space of discrete-time SwPNs can be computed directly by using existing tools for classical Petri nets; 4) we can verify temporal properties on a SwPN by working on the classical Petri net resulting from the translation. We give experimental results comparing the discrete-time state space computation and the dense-time one showing that, in many cases, combinatory explosion is not such a big concern. For the sake of simplicity, our results are explained on a model whose high-level functions make them very convenient to understand: time Petri nets with flush arcs and inhibitor hyperarcs (FIHTPNs). Our conclusions can however be easily extended to the general class of SwPNs