Complexity of Rule Redundancy in Non-ground Answer-Set Programming over Finite Domains

Recent research in answer-set programming (ASP) is concerned with the problem of finding faithful transformations of logic programs under the stable semantics. This is in particular relevant in practice when programs with variables are considered, where such transformations play a basic role in (offline) simplifications of logic programs. So far, such transformations of non-ground programs have been considered under the implicit assumption that the domain (i.e., the set of constants of the underlying language) is always suitably extensible. However, this may not be a desired scenario, e.g., if one needs to deal with a fixed number of objects. In this paper, we investigate how an explicit restriction of the domain influences the applicability of program transformations and we study in detail computational aspects for the concepts of tautological rules and rule subsumption. More precisely, we provide a full picture of the complexity to decide whether a non-ground rule is tautological or subsumed by another rule under sev-