Anti-unification Algorithms and Their Applications in Program Analysis

摘要

A term t is called a template of terms t_1and t_2 iff t_1 = tη_1 and t_2 = tη_2, for some substitutions η_1 and η_2. A template t of t_1 and t_2 is called the most specific iff for any template t' of t_1 and t_2 there exists a substitution ξ such that t = t'ξ. The anti-unification problem is that of computing the most specific template of two given terms. This problem is dual to the well-known unification problem, which is the computing of the most general instance of terms. Unification is used extensively in automatic theorem proving and logic programming. We believe that anti-unification algorithms may have wide applications in program analysis. In this paper we present an efficient algorithm for computing the most specific templates of terms represented by labelled directed acyclic graphs and estimate the complexity of the anti-unification problem. We also describe techniques for invariant generation and software clone detection based on the concepts of the most specific templates and anti-unification.