Enhancing Predicate Pairing with Abstraction for Relational Verification

TL;DR

This paper improves relational verification by integrating abstraction techniques into predicate pairing transformations, leveraging convex polyhedra domains to enhance the inference of relations between program fragments.

Contribution

It introduces an algorithm that combines predicate pairing with linear arithmetic abstractions, demonstrated through extensive experiments using VeriMAP, PPL, and Z3.

Findings

Enhanced relational verification capabilities with abstraction.

Successful application to over a hundred problems.

Improved inference of relations among program arguments.

Abstract

Relational verification is a technique that aims at proving properties that relate two different program fragments, or two different program runs. It has been shown that constrained Horn clauses (CHCs) can effectively be used for relational verification by applying a CHC transformation, called predicate pairing, which allows the CHC solver to infer relations among arguments of different predicates. In this paper we study how the effects of the predicate pairing transformation can be enhanced by using various abstract domains based on linear arithmetic (i.e., the domain of convex polyhedra and some of its subdomains) during the transformation. After presenting an algorithm for predicate pairing with abstraction, we report on the experiments we have performed on over a hundred relational verification problems by using various abstract domains. The experiments have been performed by using the VeriMAP transformation and verification system, together with the Parma Polyhedra Library (PPL) and the Z3 solver for CHCs.