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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 thatua2v ∈ L if and only if uav ∈ L, for each u,v ∈ A*, a ∈ A.Varieties of literally idempotent languages result naturally by takingall literally idempotent languages in a classical (positive) varietyor by considering a certain closure operator on classes of languages.We initiate the systematic study of such varieties. Various classes ofliterally idempotent languages can be characterized using syntactic methods.A starting example is the classof all finite unions of $B^*_1 B^*_2\dots B^*_k$ where B1,...,Bk aresubsets of a given alphabet A.

Keywords

Literally idempotent languagesvarieties of languages.

Information

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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