Constraint-based Relational Verification

TL;DR

This paper introduces a novel automated constraint-based approach for relational verification using pfwCSP, capable of expressing complex properties beyond traditional CHCs, and demonstrates its effectiveness on challenging problems.

Contribution

It proposes a new class of predicate CSPs called pfwCSP, enabling the expression and automatic verification of advanced relational properties beyond $k$-safety.

Findings

Successfully verified complex relational properties beyond previous frameworks.

Implemented a constraint solving method based on stratified CEGIS.

Achieved promising results on diverse challenging verification problems.

Abstract

In recent years they have been numerous works that aim to automate relational verification. Meanwhile, although Constrained Horn Clauses (CHCs) empower a wide range of verification techniques and tools, they lack the ability to express hyperproperties beyond $k$-safety such as generalized non-interference and co-termination. This paper describes a novel and fully automated constraint-based approach to relational verification. We first introduce a new class of predicate Constraint Satisfaction Problems called pfwCSP where constraints are represented as clauses modulo first-order theories over predicate variables of three kinds: ordinary, well-founded, or functional. This generalization over CHCs permits arbitrary (i.e., possibly non-Horn) clauses, well-foundedness constraints, functionality constraints, and is capable of expressing these relational verification problems. Our approach enables us to express and automatically verify problem instances that require non-trivial (i.e., non-sequential and non-lock-step) self-composition by automatically inferring appropriate schedulers (or alignment) that dictate when and which program copies move. To solve problems in this new language, we present a constraint solving method for pfwCSP based on stratified CounterExample-Guided Inductive Synthesis (CEGIS) of ordinary, well-founded, and functional predicates. We have implemented the proposed framework and obtained promising results on diverse relational verification problems that are beyond the scope of the previous verification frameworks.