LITERALLY IDEMPOTENT LANGUAGES AND THEIR VARIETIES — TWO LETTER CASE

Author:

KLÍMA ONDŘEJ1,POLÁK LIBOR1

Affiliation:

1. Department of Mathematics, Masaryk University, Kotlářská 2, 611 37 Brno, Czech Republic

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. We already studied classes of such languages closely related to the (positive) varieties of the famous Straubing-Thérien hierarchy. In the present paper we start a systematic study of literal varieties of literally idempotent languages, namely we deal with the case of two letter alphabet. First, we consider natural canonical expressions for such languages. Secondly, we describe all possible classes of the form [Formula: see text] where [Formula: see text] is a literal variety of literally idempotent languages. At the end we consider also positive literal varieties of literally idempotent languages.

Publisher

World Scientific Pub Co Pte Lt

Subject

Computer Science (miscellaneous)

Reference6 articles.

1. On Varieties of Literally Idempotent Languages

2. Equational description of pseudovarieties of homomorphisms

3. L. Polák, Contribution to General Algebra 16 (Verlag Johannes Heyn, 2005) pp. 173–188.

4. Varieties of Formal Languages

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