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- W4288633265 abstract "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 most $N$, where the number $N$ depends on the arities of basic operations of the algebra and the size of the basic set. For finite idempotent algebras we give a tight bound on $N$ that, in the special case of algebras with more than $binom{|A|}2$ basic operations, improves an earlier result of K. Kearnes and A. Szendrei. On the algorithmic side, we show that deciding the existence of cube terms is in P for idempotent algebras and in EXPTIME in general. Since an algebra contains a $k$-ary near unanimity operation if and only if it contains a $k$-dimensional cube term and generates a congruence distributive variety, our algorithm also lets us decide whether a given finite algebra has a near unanimity operation." @default.
- W4288633265 created "2022-07-30" @default.
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- W4288633265 date "2019-01-15" @default.
- W4288633265 modified "2023-09-29" @default.
- W4288633265 title "Existence of cube terms in finite algebras" @default.
- W4288633265 doi "https://doi.org/10.48550/arxiv.1901.04975" @default.
- W4288633265 hasPublicationYear "2019" @default.
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