On the centers of a language |
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| Authors: | Aldo De Luca Antonio Restivo Sergio Salemi |
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| Affiliation: | Istituto di Matematica dell'' Università di Napoli, e G.N.S.A.G.A. del C.N.R., Italy;Istituto di Matematica dell'' Universitá di Palermo, e Istituto di Fisica Cosmica e Informatica del C.N.R., Italy |
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| Abstract: | The center of a language has been defined in 7, 8, 9] as the set of all words which have infinite right completions in the language. In this paper we extend this notion by taking into account also left and two-sided completions. Thus, for any language X, we consider the left center Cl(X), the right center Cr(X) and two different bilateral centers C1(X) and C2(X). Some properties of these centers are derived. In particular the main results of the paper give some general conditions under which C1(X)=C2(X)and Cr(Cl(X))=Cl(Cr(X)). These conditions deal with ‘strong’ and ‘weak’ iteration properties and ‘periodicity’ of a language. |
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