Deciding the existence of minority terms

01/02/2019

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by   Alexandr Kazda, et al.

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Lomonosov Moscow State University

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Durham University

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McMaster University

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This paper investigates the computational complexity of deciding if a given finite idempotent algebra has a ternary term operation m that satisfies the minority equations m(y,x,x) ≈ m(x,y,x) ≈ m(x,x,y) ≈ y. We show that a common polynomial-time approach to testing for this type of condition will not work in this case and that this decision problem lies in the class NP.