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 $\omega$-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 $\omega$-set decipherable languages which are very close to the $\omega$-codes. We solve the problem in the restricted case where $L$ is $\omega$-set decipherable and $L^*$ is the greatest generator of $L^\omega$.