On the Complexity of Proving Polyhedral Reductions
For researchers working on Petri net verification, this provides an automated method for proving polyhedral reductions, which are useful for reachability analysis.
The paper proposes an automated procedure to prove polyhedral abstractions for Petri nets, encoding the equivalence problem into SMT formulas and exploiting a connection with flat nets. The method is implemented and demonstrated on several examples.
We propose an automated procedure to prove polyhedral abstractions (also known as polyhedral reductions) for Petri nets. Polyhedral abstraction is a new type of state space equivalence, between Petri nets, based on the use of linear integer constraints between the marking of places. In addition to defining an automated proof method, this paper aims to better characterize polyhedral reductions, and to give an overview of their application to reachability problems. Our approach relies on encoding the equivalence problem into a set of SMT formulas whose satisfaction implies that the equivalence holds. The difficulty, in this context, arises from the fact that we need to handle infinite-state systems. For completeness, we exploit a connection with a class of Petri nets, called flat nets, that have Presburger-definable reachability sets. We have implemented our procedure, and we illustrate its use on several examples.