Towards Implementations for Advanced Equivalence Checking in Answer-Set Programming

Abstract

In recent work, a general framework for specifying program correspondences under the answer-set semantics has been defined. The framework allows to define different notions of equivalence, including the well-known notions of strong and uniform equivalence, as well as refined equivalence notions based on the projection of answer sets, where not all parts of an answer set are of relevance (like, e.g., removal of auxiliary letters). In the general case, deciding the correspondence of two programs lies on the fourth level of the polynomial hierarchy and therefore this task can (presumably) not be efficiently reduced to answer-set programming. In this paper, we describe an approach to compute program correspondences in this general framework by means of linear-time constructible reductions to quantified propositional logic. We can thus use extant solvers for the latter language as back-end inference engines for computing program correspondence problems. We also describe how our translations provide a method to construct counterexamples in case a program correspondence does not hold.