Approaching the Coverability Problem Continuously

TL;DR

This paper introduces a novel method for solving the Petri net coverability problem by combining continuous Petri net analysis with SMT encoding, significantly improving efficiency and success rate on benchmark instances.

Contribution

It presents a new approach that integrates continuous Petri net coverability with SMT-based encoding, enabling more efficient and scalable verification of concurrent programs.

Findings

Decides more instances than existing tools.

Often much faster on large instances.

Effective on standard benchmarks.

Abstract

The coverability problem for Petri nets plays a central role in the verification of concurrent shared-memory programs. However, its high EXPSPACE-complete complexity poses a challenge when encountered in real-world instances. In this paper, we develop a new approach to this problem which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. A cornerstone of our approach is the efficient encoding of a recently developed polynomial-time algorithm for reachability in continuous Petri nets into SMT. We demonstrate the effectiveness of our approach on standard benchmarks from the literature, which shows that our approach decides significantly more instances than any existing tool and is in addition often much faster, in particular on large instances.