2011/02/17 by Émilie Charlier, Narad Rampersad, Charlier, Emilie +3
Computer Science · #Algorithms and Data Compression #Computability, Logic, AI Algorithms #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1102.3698
openalex publication_date 2011/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.