Reading functions and an extension of Kleene theorem for some families of languages
A reading function is defined as f : σ* → σ*, where σ is an alphabet. By means of reading functions and the family of regular languages, new families of languages can be defined. In the paper we study properties of the so called permutation type reeding functions. For finitely generated functions of this type the set of basic functions is constructed. Some of these functions generate families of languages properly containing regular sets and having algebraic properties similar to regular languages. An extension of Kleene theorem for families of languages generated by bijective reading functions is presented.
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