A Polyhedral Abstraction for Petri nets and its Application to SMT-Based Model Checking

TL;DR

This paper introduces a polyhedral abstraction method for Petri nets that enhances SMT-based model checking by reducing net complexity, proven correct through a new equivalence notion, and implemented in the SMPT tool with successful experimental results.

Contribution

It presents a novel polyhedral abstraction technique for Petri nets, along with a framework for correctness and an implementation that improves model checking efficiency.

Findings

Effective reduction of Petri nets improves model checking performance.

The method is validated on a large set of queries from the Model Checking Contest.

SMPT demonstrates practical benefits even with moderate reductions.

Abstract

We define a new method for taking advantage of net reductions in combination with a SMT-based model checker. Our approach consists in transforming a reachability problem about some Petri net, into the verification of an updated reachability property on a reduced version of this net. This method relies on a new state space abstraction based on systems of constraints, called polyhedral abstraction. We prove the correctness of this method using a new notion of equivalence between nets. We provide a complete framework to define and check the correctness of equivalence judgements; prove that this relation is a congruence; and give examples of basic equivalence relations that derive from structural reductions. Our approach has been implemented in a tool, named SMPT, that provides two main procedures: Bounded Model Checking (BMC) and Property Directed Reachability (PDR). Each procedure has been adapted in order to use reductions and to work with arbitrary Petri nets. We tested SMPT on a large collection of queries used in the Model Checking Contest. Our experimental results show that our approach works well, even when we only have a moderate amount of reductions.