Displaying similar documents to “A conjecture on the concatenation product”

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...

On Varieties of Literally Idempotent Languages

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...

Imre Simon : an exceptional graduate student

Denis Thérien (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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This short note reviews the main contributions of the Ph.D. thesis of Imre Simon. His graduate work had major impact on algebraic theory of automata and thirty years later we are in a good position to appreciate how sensitive he was in selecting good problems, and how clever in solving them!

Polynomial languages with finite antidictionaries

Arseny M. Shur (2008)

RAIRO - Theoretical Informatics and Applications

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We tackle the problem of studying which kind of functions can occur as complexity functions of formal languages of a certain type. We prove that an important narrow subclass of rational languages contains languages of polynomial complexity of any integer degree over any non-trivial alphabet.

Classes of two-dimensional languages and recognizability conditions

Marcella Anselmo, Maria Madonia (2011)

RAIRO - Theoretical Informatics and Applications

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The paper deals with some classes of two-dimensional recognizable languages of “high complexity”, in a sense specified in the paper and motivated by some necessary conditions holding for recognizable and unambiguous languages. For such classes we can solve some open questions related to unambiguity, finite ambiguity and complementation. Then we reformulate a necessary condition for recognizability stated by Matz, introducing a new complexity function. We solve an open question proposed...