Equality sets for recursively enumerable languages
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 39 (2005) no. 4, pp. 661-675.

We consider shifted equality sets of the form E G (a,g 1 ,g 2 )={wg 1 (w)=ag 2 (w)}, where g 1 and g 2 are nonerasing morphisms and a is a letter. We are interested in the family consisting of the languages h(E G (J)), where h is a coding and E G (J) is a shifted equality set. We prove several closure properties for this family. Moreover, we show that every recursively enumerable language LA * is a projection of a shifted equality set, that is, L=π A (E G (a,g 1 ,g 2 )) for some (nonerasing) morphisms g 1 and g 2 and a letter a, where π A deletes the letters not in A. Then we deduce that recursively enumerable star languages coincide with the projections of equality sets.

DOI: 10.1051/ita:2005035
Classification: 03D25,  68Q45
Keywords: morphism, equality set, shifted post correspondence problem, closure properties, recursively enumerable sets
Halava, Vesa ; Harju, Tero ; Hoogeboom, Hendrik Jan 1; Latteux, Michel 2

1 Department of Computer Science, Leiden University PO Box 9512, 2300 RA Leiden, The Netherlands;
2 Université des Sciences et Technologies de Lille, Bâtiment M3, 59655 Villeneuve d’Ascq Cedex, France
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Halava, Vesa; Harju, Tero; Hoogeboom, Hendrik Jan; Latteux, Michel. Equality sets for recursively enumerable languages. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 39 (2005) no. 4, pp. 661-675. doi : 10.1051/ita:2005035. http://www.numdam.org/articles/10.1051/ita:2005035/

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