ON ULTIMATELY PERIODIC WORDS OF RATIONAL OMEGA-LANGUAGES

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.