Equality sets for recursively enumerable languages

Vesa Halava, Tero Harju, Hendrik Jan Hoogeboom, Michel Latteux
2005 RAIRO - Theoretical Informatics and Applications  
We consider shifted equality sets of the form EG(a, g1, g2) = {w | g1(w) = ag2(w)}, where g1 and g2 are nonerasing morphisms and a is a letter. We are interested in the family consisting of the languages h(EG(J)), where h is a coding and EG(J) is a shifted equality set. We prove several closure properties for this family. Moreover, we show that every recursively enumerable language L ⊆ A * is a projection of a shifted equality set, that is, L = πA (EG(a, g1, g2) ) for some (nonerasing)
more » ... onerasing) morphisms g1 and g2 and a letter a, where πA deletes the letters not in A. Then we deduce that recursively enumerable star languages coincide with the projections of equality sets. Mathematics Subject Classification. 03D25, 68Q45. Article published by EDP Sciences and available at http://www.edpsciences.org/ita or http://dx.
doi:10.1051/ita:2005035 fatcat:piirxi2xhze2rhhltbgwztj4zi