Petri Net Invariant Synthesis

TL;DR

This paper introduces a new method for synthesizing inductive half spaces as invariants in Petri nets, using a CEGAR-loop and linear constraints, to improve disproving reachability and coverability.

Contribution

It formulates a structure theory for inductive half spaces and develops a CEGAR-based synthesis approach with an implementation that outperforms existing techniques.

Findings

The synthesis method is effective in disproving reachability.

The approach is competitive with state-of-the-art tools.

Deciding inductiveness is coNP-complete.

Abstract

We study the synthesis of inductive half spaces (IHS). These are linear inequalities that form inductive invariants for Petri nets, capable of disproving reachability or coverability. IHS generalize classic notions of invariants like traps or siphons. Their synthesis is desirable for disproving reachability or coverability where traditional invariants may fail. We formulate a CEGAR-loop for the synthesis of IHS. The first step is to establish a structure theory of IHS. We analyze the space of IHS with methods from discrete mathematics and derive a linear constraint system closely over-approximating the space. To discard false positives, we provide an algorithm that decides whether a given half space is indeed inductive, a problem that we prove to be coNP-complete. We implemented the CEGAR-loop in the tool INEQUALIZER and our experiments show that it is competitive against state-of-the-art techniques.