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In computational complexity theory, a branch of computer science, Schaefer's dichotomy theorem, proved by Thomas Jerome Schaefer, states necessary and sufficient conditions under which a finite set S of relations over the Boolean domain yields polynomial-time or NP-complete problems when the relations of S are used to constrain some of the propositional variables.
It is called a dichotomy theorem because the complexity of the problem defined by S is either in P or is NP-complete, as opposed to one of the classes of intermediate complexity that is known to exist by Ladner's theorem.
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