Locally consistent constraint satisfaction problems (extended abstract)

Abstract

An instance of a constraint satisfaction problem is l-consistent if any l constraints of it can be simultaneously satisfied. For a fixed constraint type P, ρl(P) denotes the largest ratio of constraints which can be satisfied in any l-consistent instance. In this paper, we study locally consistent constraint satisfaction problems for constraints which are Boolean predicates. We determine the values of ρl(P) for all l and all Boolean predicates which have a certain natural property which we call 1-extendibility as well as for all Boolean predicates of arity at most three. All our results hold for both the unweighted and weighted versions of the problem. © Springer-Verlag Berlin Heidelberg 2004.