Test sets for languages of infinite words (Q1113683)

The paper proves the following generalization of the Ehrenfeucht conjecture to the case of \(\infty\)-languages, that is, to sets containing words of possibly both finite and infinite length: Let A be a finite alphabet. For each \(\infty\)-language \(L\subseteq A^{\infty}\) there is a finite subset \(F\subseteq L\) such that whenever two morphisms f, g mapping \(A^*\) into a countably generated free monoid coincide on F then they also coincide on the whole \(\infty\)-language L.