We show that the subword complexity function ρx (n), which counts the number of distinct factors of length n of a sequence x, is k-synchronized in the sense of Carpi if x is k-automatic. As an application, we generalize recent results of Goldstein. We give analogous results for the number of distinct factors of length n that are primitive words or powers. In contrast, we show that the function that counts the number of unbordered factors of length n is not necessarily k-synchronized for k-automatic sequences. © 2013 Springer-Verlag.
CITATION STYLE
Goč, D., Schaeffer, L., & Shallit, J. (2013). Subword complexity and k-synchronization. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7907 LNCS, pp. 252–263). https://doi.org/10.1007/978-3-642-38771-5_23
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