Displaying similar documents to “Equations on the semidirect product of a finite semilattice by a 𝒥 -trivial monoid of height k ”

Varieties of finite categories

Alex Weiss, Denis Therien (1986)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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Some results on 𝒞 -varieties

Jean-Éric Pin, Howard Straubing (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In an earlier paper, the second author generalized Eilenberg’s variety theory by establishing a basic correspondence between certain classes of monoid morphisms and families of regular languages. We extend this theory in several directions. First, we prove a version of Reiterman’s theorem concerning the definition of varieties by identities, and illustrate this result by describing the identities associated with languages of the form ( a 1 a 2 ⋯ a k ) + , where a 1 , ... , a k are distinct letters. Next, we generalize...

A conjecture on the concatenation product

Jean-Eric Pin, Pascal Weil (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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In a previous paper, the authors studied the polynomial closure of a variety of languages and gave an algebraic counterpart, in terms of Mal’cev products, of this operation. They also formulated a conjecture about the algebraic counterpart of the boolean closure of the polynomial closure – this operation corresponds to passing to the upper level in any concatenation hierarchy. Although this conjecture is probably true in some particular cases, we give a counterexample in the general...