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Deciding absorption

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 Added by Alexandr Kazda
 Publication date 2015
and research's language is English




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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.



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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 time when the algebras tested are idempotent and the Maltsev condition $Sigma$ can be described using paths. Examples of such path conditions are having a Maltsev term, having a majority operation, and having a chain of Jonsson (or Gumm) terms of fixed length.
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