From local to global consistency

摘要

In reasoning tasks involving the maintenance of consistent databases (so-called QQconstraint networks/Q/Q), it is customary to enforce local consistency conditions in order to simplify the subsequent construction of a globally coherent model of the data. In this paper we present a relationship between the sizes of the variables' domains, the constraints' arity and the level of local consistency sufficient to ensure global consistency. Based on these parameters a new tractability classification of constraint networks is presented. We also show, based on this relationship, that any relation on bi-valued variables which is not representable by a network of binary constraints cannot be represented by networks with any number of hidden variables.