Reformulating Positive Table Constraints Using Functional Dependencies

Constraints that are defined by tables of allowed tuples of assignments are common in constraint programming. In this paper we present an approach to reformulating table constraints of large arity into a conjunction of lower arity constraints. Our approach exploits functional dependencies. We study the complexity of finding reformulations that either minimize the memory size or arity of a constraint using a set of its functional dependencies. We also present an algorithm to compute such reformulations. We show that our technique is complementary to existing approaches for compressing extensional constraints.