A Toolchain to Compute Concurrent Places of Petri Nets

Abstract

The concurrent places of a Petri net are all pairs of places that may simultaneously have a token in some reachable marking. Concurrent places generalize the usual notion of dead places and are particularly useful for decomposing a Petri net into synchronized automata executing in parallel. We present a state-of-the-art toolchain to compute the concurrent places of a Petri net. This is achieved by a rich combination of various techniques, including: state-space exploration using BDDs, structural rules for concurrent places, quadratic over- and under-approximation of reachable markings, and polyhedral abstraction of the state space based on structural reductions and linear arithmetic constraints on markings. We assess the performance of our toolchain on a large collection of 850 nets originating from the 2022 edition of the Model Checking Contest.