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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 $m(y,x,x) approx m(x,y,x) approx m(x,x,y) approx y$. 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.
We show that for a fixed positive integer k one can efficiently decide if a finite algebra A admits a k-ary weak near unanimity operation by looking at the local behavior of the terms of A. We also observe that the problem of deciding if a given fini
We study the problem of whether a given finite algebra with finitely many basic operations contains a cube term; we give both structural and algorithmic results. We show that if such an algebra has a cube term then it has a cube term of dimension at
We study the computational complexity of deciding whether a given set of term equalities and inequalities has a solution in an $omega$-categorical algebra $mathfrak{A}$. There are $omega$-categorical groups where this problem is undecidable. We show
We characterize absorption in finite idempotent algebras by means of Jonsson absorption and cube term blockers. As an application we show that it is decidable whether a given subset is an absorbing subuniverse of an algebra given by the tables of its basic operations.
In this paper we investigate the computational complexity of deciding if a given finite algebraic structure satisfies a fixed (strong) Maltsev condition $Sigma$. Our goal in this paper is to show that $Sigma$-testing can be accomplished in polynomial