Arc Consistency Algorithms via Iterations of Subsumed Functions
We provide here an extension of a general framework introduced in [Apt99b,Apt99c] that allows to explain several local consistency algorithms in a systematic way. In this framework we proceed in two steps. First, we introduce a generic iteration algorithm on partial orderings and prove its correctness. Then we instantiate this algorithm with specific partial orderings and functions to obtain specific local consistency algorithms. In particular, using the notion of subsumption, we show that the algorithms AC4, HAC-4, AC-5 and our extension HAC-5 of AC-5 are instances of a single generic algorithm.
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