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