Languajes and monoids with disjuntive identity.
Lila Kari, Gabriel Thierrin (1995)
Collectanea Mathematica
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Lila Kari, Gabriel Thierrin (1995)
Collectanea Mathematica
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Janusz A. Brzozowski (1974-1975)
Séminaire Dubreil. Algèbre et théorie des nombres
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Janusz A. Brzozowski (1976)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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Ondřej Klíma, Libor Polák (2008)
RAIRO - Theoretical Informatics and Applications
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A language is literally idempotent in case that if and only if , for each , . Varieties of literally idempotent languages result naturally by taking all literally idempotent languages in a classical (positive) variety or by considering a certain closure operator on classes of languages. We initiate the systematic study of such varieties. Various classes of literally idempotent languages can be characterized using syntactic methods. A starting example is the class of all finite unions...
Gerard Lallement (1989)
Semigroup forum
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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...
Zoltán Ésik, Kim G. Larsen (2003)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages.
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 , where are distinct letters. Next, we generalize...