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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 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) 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.

Keywords

Morphismequality setshifted Post Correspondence Problemclosure propertiesrecursively enumerable sets.
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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