| Summary: | In this work we discuss the consistency of constraints for which the set of solutions can be recognised by a deterministic finite automaton. Such an automaton induces a decomposition of the constraint into a conjunction of constraints. Since the level of filtering for the conjunction of constraints is not known, at any point during search there might be only one possible solution but, since all impossible values might not have yet been removed, we could be wasting time looking at impossible combinations of values. The so far most general result is that if the constraint hypergraph of such a decomposition is Berge-acyclic, then the decomposition provides hyper-arc consistency, which means that the decomposition achieves the best possible filtering. We focus our work on constraint networks that have alpha-acyclic, centred-cyclic or sliding-cyclic hypergraph representations. For each of these kinds of constraints networks we show systematically the necessary conditions to achieve hyper-arc consistency.
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