Equality sets of prefix morphisms and regular star languages

Authors:
Vesa Halava;Tero Harju;Michel Latteux
Affiliations:
Department of Mathematics and TUCS--Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland;Department of Mathematics and TUCS--Turku Centre for Computer Science, University of Turku, FIN-20014 Turku, Finland;Université des sciences et technologies de Lille, bâtiment M3, 59655 Villeneuve d'Ascq cedex, France
Venue:
Information Processing Letters
Year:
2005

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Abstract

We consider equality sets of prefix morphisms, that is, sets E(g1, g2) = {w| g1(w) = g2(w)}, where g1 and g2 are prefix morphisms. Recall that a morphism g is prefix if, for all different letters a and b, g(a) is not a prefix of g(b). We prove a rather surprising equality on families of languages, namely, that the family of regular star languages coincides with the family of languages of form πA(E(g1, g2)) for some prefix morphisms g1 and g2, and a projection πA which deletes the letters not in A.