#####
Séminaire Lotharingien de Combinatoire, B19f (1988).

[Formerly: Publ. I.R.M.A. Strasbourg, 1988, 361/S-19, p.
113-115.]

# Aldo de Luca

# On the Existence of a Finite Base for Systems of
Equations of Infinite Words

**Abstract.**
We prove that any set of equations on infinite words in a finite
number of indeterminates has, over a countably generated free
monoid,
a finite equivalent subsystem. From this it follows that any language
*L* of finite and infinite words on a finite alphabet *A* has
a test set for
morphisms from *A*^{\infty} to
*B*^{\infty}.
In the case of finite
words, the result was proved by M. H. Albert and J. Lawrence.

The paper has been finally published under the title
"Test sets for languages of infinite words" in
*Inform. Process. Lett.* **29** (1988), 91-95.