Automatic Generation of Constraint Propagation Algorithms for Small Finite Domains

Abstract

We study here constraint satisfaction problems that are based on predefined, explicitly given finite constraints. To solve them we propose a notion of rule consistency that can be expressed in terms of rules derived from the explicit representation of the initial constraints. This notion of local consistency is weaker than arc consistency for constraints of arbitrary arity but coincides with it when all domains are unary or binary. For Boolean constraints rule consistency coincides with the closure under the well-known propagation rules for Boolean constraints. By generalizing the format of the rules we obtain a characterization of arc consistency in terms of so-called inclusion rules. The advantage of rule consistency and this rule based characterization of the arc consistency is that the algorithms that enforce both notions can be automatically generated, as CHR rules. So these algorithms could be integrated into constraint logic programming systems such as Eclipse. We illustrate the usefulness of this approach to constraint propagation by discussing the implementations of both algorithms and their use on various examples, including Boolean constraints, three valued logic of Kleene, constraints dealing with Waltz's language for describing polyhedreal scenes, and Allen's qualitative approach to temporal logic.