Interpolant Tree Automata and their Application in Horn Clause Verification

TL;DR

This paper presents a novel combination of interpolant tree automata with abstract interpretation over convex polyhedra to improve Horn clause verification, generalizing spurious counterexamples and enhancing verification power.

Contribution

It introduces a new method that combines interpolant tree automata with abstract interpretation for Horn clause verification, improving generalization of counterexamples.

Findings

Improved verification power with combined approach

Some performance overhead observed

Effective in eliminating spurious counterexamples

Abstract

This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way in this paper. The role of an interpolant tree automaton is to provide a generalisation of a spurious counterexample during refinement, capturing a possibly infinite set of spurious counterexample traces. In our approach these traces are then eliminated using a transformation of the Horn clauses. We compare this approach with two other methods; one of them uses interpolant tree automata in an algorithm for trace abstraction and refinement, while the other uses abstract interpretation over the domain of convex polyhedra without the generalisation step. Evaluation of the results of experiments on a number of Horn clause verification problems indicates that the combination of interpolant tree automaton with abstract interpretation gives some increase in the power of the verification tool, while sometimes incurring a performance overhead.