Simple interpolants for linear arithmetic

Abstract

Craig interpolation has turned out to be an essential method for many applications in formal verification. In this paper we focus on the computation of simple interpolants for the theory of linear arithmetic with rational coefficients. We successfully minimize the number of linear constraints in the final interpolant by several methods including proof transformations, linear programming, and SMT solving. Experimental results comparing the approach to standard methods from the literature prove the effectiveness of the approach and show reductions of up to 70% in the number of linear constraints.