POWERS OF REGULAR LANGUAGES
Szilárd Zsolt Fazekas · International Journal of Foundations of Computer Science · 2011
In this paper we prove that it is decidable whether the set pow (L), which we get by taking all the powers of all the words in some regular language L, is regular or not. The problem was originally posed by Calbrix and Nivat in 1995. Partial solutions have been given by Cachat for unary languages and by Horváth et al. for various kinds of exponent sets for the powers and regular languages which have primitive roots satisfying certain properties. We show that the regular languages which have a regular power are the ones which are 'almost' equal to their Kleene-closure.