Local Consistency on Conjunctions of Constraints

Constraint networks are used more and more to solve combinatorial problems in real-life applications. As pointed out in BR97], this success requires dealing with non-binary constraints, which are widely needed in real world constraint solvers. Since arc consistency is a fundamental piece of reasoning that seems to be of great help during search for solutions, it is important to have eecient arc consistency algorithms for non-binary constraints. In BR97], a rst step has been done, resulting in a general schema for arc consistency on any kind of constraints, and in instantiations of the schema to handle the more general non-binary constraints, i.e., those given as a predicate or as a set of allowed/forbidden combinations of values. In this paper, we extend that work by proposing an eecient way to compute local consistency on conjunctions of constraints (called conjunctive consistency). We then use this notion to improve arc consistency processing on two practical cases, embedding constraints, which can be found in any network, and conjunctive constraints, which are often present in problems modelization.