Some Remarks on Almost Periodic Sequences and Languages

Almost periodicity has been considered in Formal Language Theory in connection with some topics in Symbolic Dynamics. In (Păun and Marcus, Bulletin of EATCS 53 (1994)) some problems concerning this property are raised. For instance it is asked whether there exists some almost periodic word $\alpha$ such that $Sub(\alpha )$, the set of its finite factors, is context-free non-regular. We answer negatively (even in a stronger form) this question, as well as discussing other related topics.