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Equality sets for recursively enumerable languages

Published online by Cambridge University Press:  15 October 2005

Vesa Halava ,
Tero Harju ,
Hendrik Jan Hoogeboom  and
Michel Latteux
Vesa Halava
Affiliation:
Department of Mathematics and TUCS – Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland; vesa.halava@utu.fi; harju@utu.fi
Tero Harju
Affiliation:
Department of Mathematics and TUCS – Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland; vesa.halava@utu.fi; harju@utu.fi
Hendrik Jan Hoogeboom
Affiliation:
Department of Computer Science, Leiden University PO Box 9512, 2300 RA Leiden, The Netherlands; hoogeboom@liacs.nl
Michel Latteux
Affiliation:
Université des Sciences et Technologies de Lille, Bâtiment M3, 59655 Villeneuve d'Ascq Cedex, France; latteux@lifl.fr
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Abstract

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.

Keywords

Morphismequality setshiftedPost Correspondence Problemclosure propertiesrecursivelyenumerable sets.

Information

Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 39 , Issue 4 , October 2005 , pp. 661 - 675
Copyright
© EDP Sciences, 2005

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