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On Varieties of Literally Idempotent Languages

Published online by Cambridge University Press:  03 June 2008

Ondřej Klíma  and
Libor Polák
Ondřej Klíma
Affiliation:
Department of Mathematics, Masaryk University, Janáčkovo nám 2a, 662 95 Brno, Czech Republic; polak@math.muni.cz
Libor Polák
Affiliation:
Department of Mathematics, Masaryk University, Janáčkovo nám 2a, 662 95 Brno, Czech Republic; polak@math.muni.cz
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Abstract

A language L ⊆A* is literally idempotent in case that ua2v ∈ L if and only if uav ∈ L, for each u,v ∈ A*, a ∈ A. 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 of $B^*_1 B^*_2\dots B^*_k$ where B1,...,Bk are subsets of a given alphabet A.

Keywords

Literally idempotent languagesvarieties of languages.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 3: JM'06 , July 2008 , pp. 583 - 598
Copyright
© EDP Sciences, 2008

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