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On Varieties of Literally Idempotent Languages
Published online by Cambridge University Press: 03 June 2008
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.
- 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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