Bottoms Up for CHCs: Novel Transformation of Linear Constrained Horn Clauses to Software Verification

TL;DR

This paper introduces a novel bottom-up transformation technique for linear Constrained Horn Clauses (CHCs) that significantly improves the efficiency of software verification compared to traditional top-down methods.

Contribution

The paper presents a new bottom-up approach for transforming linear CHCs and demonstrates its effectiveness within the THETA model checking framework, outperforming existing top-down methods.

Findings

Over twofold increase in tasks solved with the bottom-up approach

Effective on both synthetic and industrial examples

Enhances verification workflow efficiency

Abstract

Constrained Horn Clauses (CHCs) have conventionally been used as a low-level representation in formal verification. Most existing solvers use a diverse set of specialized techniques, including direct state space traversal or under-approximating abstraction, necessitating purpose-built complex algorithms. Other solvers successfully simplified the verification workflow by translating the problem to inputs for other verification tasks, leveraging the strengths of existing algorithms. One such approach transforms the CHC problem into a recursive program roughly emulating a top-down solver for the deduction task; and verifying the reachability of a safety violation specified as a control location. We propose an alternative bottom-up approach for linear CHCs, and evaluate the two options in the open-source model checking framework THETA on both synthetic and industrial examples. We find that there is a more than twofold increase in the number of solved tasks when the novel bottom-up approach is used in the verification workflow, in contrast with the top-down technique.