H. Calbrix et al., ON ULTIMATELY PERIODIC WORDS OF RATIONAL OMEGA-LANGUAGES, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 318(5), 1994, pp. 493-497
We're starting from the fact that a rational omega-language is caracte
rized by the set of its ultimately periodic words. These words may be
represented by finite ones. We define the language L($) of these repre
sentations and we show that it is a rational language. Then, we charac
terize rational languages which are obtained by this mean. Our proofs
of these two results are constructive. Finally, we prove the equality
between syntactic congruences of L and L($), and this provides us a wa
y to build the syntactic congruence of L.