Set decipherable languages and generators

Abstract

We investigate the problem to characterize whether the infinite product of a given language L is generated by an ω-code. Up to now, this problem is open even if language L is a finite language. In this work, we consider a class of languages named ω-set decipherable languages which are very close to the ω-codes. We solve the problem in the restricted case where L is ω-set decipherable and L* is the greatest generator of Lω.