Sharper and Simpler Nonlinear Interpolants for Program Verification

TL;DR

This paper introduces an improved method for generating sharper and simpler nonlinear interpolants using real algebraic geometry and a continued fraction-based algorithm, enhancing program verification techniques.

Contribution

It presents a novel enhancement that produces more precise and simpler interpolants by combining real algebraic geometry insights with a continued fraction algorithm for SDP solutions.

Findings

Enhanced interpolants improve verification accuracy

The method produces sharper, simpler interpolants

Experimental results validate effectiveness in verification tasks

Abstract

Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhancement is made possible by: theoretical observations in real algebraic geometry; and our continued fraction-based algorithm that rounds off (potentially erroneous) numerical solutions of SDP solvers. Experiment results support our tool's effectiveness; we also demonstrate the benefit of sharp and simple interpolants in program verification examples.