On Varieties of Literally Idempotent Languages
Department of Mathematics, Masaryk University,
Janáčkovo nám 2a, 662 95 Brno, Czech Republic; email@example.com
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 where B1,...,Bk are subsets of a given alphabet A.
Mathematics Subject Classification: 68Q45
Key words: Literally idempotent languages / varieties of languages.
© EDP Sciences, 2008