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Enumeration and Decidable Properties of Automatic Sequences

By Emilie Charlier, Narad Rampersad and Jeffrey Shallit


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 some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Topics: Computer Science - Formal Languages and Automata Theory, Computer Science - Discrete Mathematics
Year: 2011
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