Directed Reachability for Infinite-State Systems

TL;DR

This paper presents a practical semi-decision method for Petri net reachability using lightweight over-approximations as distance oracles, significantly improving efficiency over existing tools.

Contribution

Introduces a novel approach leveraging over-approximations as distance oracles for efficient Petri net reachability analysis, with a practical implementation.

Findings

Prototype outperforms state-of-the-art tools

Achieves orders-of-magnitude speedups in some cases

Competitive with domain-specific tools on benchmarks

Abstract

Numerous tasks in program analysis and synthesis reduce to deciding reachability in possibly infinite graphs such as those induced by Petri nets. However, the Petri net reachability problem has recently been shown to require non-elementary time, which raises questions about the practical applicability of Petri nets as target models. In this paper, we introduce a novel approach for efficiently semi-deciding the reachability problem for Petri nets in practice. Our key insight is that computationally lightweight over-approximations of Petri nets can be used as distance oracles in classical graph exploration algorithms such as A* and greedy best-first search. We provide and evaluate a prototype implementation of our approach that outperforms existing state-of-the-art tools, sometimes by orders of magnitude, and which is also competitive with domain-specific tools on benchmarks coming from program synthesis and concurrent program analysis.