This paper presents a complete classification of the complexity of the SAT and equivalence problems for two-element algebras. Cases of terms and polynomials are considered. We show that for any fixed two-element algebra the considered SAT problems are either in P or NP-complete and the equivalence problems are either in P or coNP-complete. We show that the complexity of the considered problems, parametrized by an algebra, are determined by the clone of term operations of the algebra and does not depend on generating functions for the clone.
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