Abstract

We present KReach, a tool for deciding reachability in general Petri nets. The tool is a full implementation of Kosaraju’s original 1982 decision procedure for reachability in VASS. We believe this to be the first implementation of its kind. We include a comprehensive suite of libraries for development with Vector Addition Systems (with States) in the Haskell programming language. KReach serves as a practical tool, and acts as an effective teaching aid for the theory behind the algorithm. Preliminary tests suggest that there are some classes of Petri nets for which we can quickly show unreachability. In particular, using KReach for coverability problems, by reduction to reachability, is competitive even against state-of-the-art coverability checkers.

Highlights

  • IntroductionPetri nets [26] (equivalently, Vector Addition Systems with States [12,14]) are one of the best-known formalisms in concurrency theory

  • Petri nets [26] are one of the best-known formalisms in concurrency theory

  • – Noting that the reachability problem is infamous for its complexity—both in terms of its worst-case runtime, and the impenetrability of its decision procedures for newcomers—we offer an accessible implementation of Kosaraju’s algorithm, which can be used as a detailed learning aid

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Summary

Introduction

Petri nets [26] (equivalently, Vector Addition Systems with States [12,14]) are one of the best-known formalisms in concurrency theory. They form a highly expressive model which is applicable in a broad range of domains including software and hardware verification [5,6], chemical modelling [3], and business processes [22]. Two of the most studied decision problems on Petri nets are those of coverability and reachability. Coverability is the central decision problem for verifying safety properties on Petri nets. The coverability problem asks, given a starting configuration m0 and a target m, whether we can reach, by some sequence of valid transitions (i.e. by a run), any configuration m′ ≥ m. Coverability has seen considerable study in recent years, in particular with a view towards minimising the running time of coverability decision procedures [2,11]

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