On varieties of literally idempotent languages

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Authors

KLÍMA Ondřej POLÁK Libor

Year of publication 2006
Type Article in Proceedings
Conference Internal Proceedings, Mons Days of Theoretical Computer Science
MU Faculty or unit

Faculty of Science

Citation
Field Informatics
Keywords literal idempotence; varieties of languages
Description A language $L\subseteq A^*$ is literally idempotent in case that $ua^2v\in L$ if and only if $uav\in L$, for each $u,v\in A^*$, $a\in A$. Such classes 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 their systematic study. Various classes of such 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 $B_1,\dots,B_k$ are subsets of a given alphabet $A$.
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