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1 results

  • Equality sets for recursively enumerable languages

  • Vesa Halava, Tero Harju, Hendrik Jan Hoogeboom, Michel Latteux
  • Journal:
    RAIRO - Theoretical Informatics and Applications / Volume 39 / Issue 4 / October 2005
    Published online by Cambridge University Press:
    15 October 2005, pp. 661-675
    Print publication:
    October 2005

  • We consider shifted equality sets of the form EG(a,g1,g2) = {ω | g1(ω) = ag2(ω)}, where g 1 and g 2 are nonerasingmorphisms and a is a letter. We are interested in the familyconsisting of the languages h(EG(J)), where h is a coding and(EG(J)) is a shifted equality set. We prove several closureproperties for this family. Moreover, we show that everyrecursively enumerable language L ⊆ A* is a projectionof a shifted equality set, that is, L = πA(EG(a,g1,g2)) for some (nonerasing) morphisms g 1 and g 2 and aletter a, where πA deletes the letters not in A. Thenwe deduce that recursively enumerable star languages coincide withthe projections of equality sets.