An algebraic characterization of tractable constraints
Many combinatorial search problems may be expressed as ‘constraint satisfaction problems’, and this class of problems is known to be NP-complete. In this paper we investigate what restrictions must be imposed on the allowed constraints in order to ensure tractability. We describe a simple algebraic closure condition, and show that this is both necessary and sufficient to ensure tractability in Boolean valued problems. We also demonstrate that this condition is necessary for problems with arbitrary finite domains.
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