Geodesic
On definability of one-symbol languages in the monoid of finite languages with concatenation
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2020), pp. 5-13

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We consider an algebra of all finite languages with the concatenation operation. For one-symbol languages it is known that its theory is equivalent to the first-order arithmetic. Earlier it was proved that for regular languages a one-symbol algebra can be interpreted in multi-symbol algebras. Here we show how to define a one-symbol subalgebra in multi-symbol algebras for finite languages.
Keywords: language, finite language, concatenation, first-order arithmetic. 
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     title = {On definability of one-symbol languages in the monoid of finite languages with concatenation},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
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S. M. Dudakov. On definability of one-symbol languages in the monoid of finite languages with concatenation. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 4 (2020), pp. 5-13. http://geodesic.mathdoc.fr/item/VTPMK_2020_4_a0/