Abstract
We present the computational complexity equivalence of Constraint Satisfaction Problem and solving systems of equations over unary algebras. We give detailed description of the polynomial transformation used both ways. We also prove that solving system of equations over arbitrary finite algebra is polynomially equivalent to solving system of equations over specially constructed unary algebra. Finally we show that if P is not equal to NP then the class of unary algebras for which solving systems of equations is solvable in a polynomial time is not closed under homomorphic images.
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Reference
Bulatov AA (2006) A dichotomy theorem for constraint satisfaction problems on a 3-element set. J ACM 53(1):66–120 (electronic)
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Broniek, P. (2015). Reducing CSP to SysTermSat over Unary Algebras. In: Computational Complexity of Solving Equation Systems. SpringerBriefs in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-319-21750-5_3
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DOI: https://doi.org/10.1007/978-3-319-21750-5_3
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