Craig Interpolation and Reachability Analysis

Abstract

A Craig interpolant for a mutually inconsistent pair of formulas (A, B) is a formula that is (1) implied by A, (2) inconsistent with B, and (3) expressed over the common variables of A and B. It is known that a Craig interpolant can be efficiently derived from a refutation of A Λ B, for a variety of theories and proof systems. This fact has been used primarily in proving lower bounds for various proof systems. In this talk, I will discuss a method that uses Craig interpolation to construct abstract image operators relative to a given property to be proved. In essence, the abstract image operator preserves just enough information to prove that the property is not violated within k steps. This provides a sound and complete procedure for reachability in transition systems of finite diameter. For infinite diameter, convergence is not guaranteed. However, the fact that the image operator is abstracted relative to a property may allow convergence in cases where an exact analysis would diverge.

This approach could have applications in software verification, as an alternative or adjunct to predicate abstraction, and to verification of “infinite state” systems in general.