Enumeration and decidable properties of automatic sequences

Abstract

We show that various aspects of k-automatic sequences - such as having an unbordered factor of length n - are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give a new characterization of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems. © 2011 Springer-Verlag.