Counterexample-Guided Prophecy for Model Checking Modulo the Theory of Arrays

TL;DR

This paper introduces a framework that enhances model checking of infinite-state systems by automatically adding auxiliary variables, enabling more efficient quantifier-free proofs for array-based systems, and demonstrates its effectiveness on benchmark problems.

Contribution

It presents a novel combination of auxiliary variable augmentation with counterexample-guided abstraction refinement for arrays, reducing complex reasoning to simpler quantifier-free logic.

Findings

Often outperforms state-of-the-art tools

Reduces reasoning complexity for array systems

Effective on diverse benchmarks

Abstract

We develop a framework for model checking infinite-state systems by automatically augmenting them with auxiliary variables, enabling quantifier-free induction proofs for systems that would otherwise require quantified invariants. We combine this mechanism with a counterexample-guided abstraction refinement scheme for the theory of arrays. Our framework can thus, in many cases, reduce inductive reasoning with quantifiers and arrays to quantifier-free and array-free reasoning. We evaluate the approach on a wide set of benchmarks from the literature. The results show that our implementation often outperforms state-of-the-art tools, demonstrating its practical potential.