Enumeration and Decidable Properties of Automatic Sequences

  • Émilie Charlier
  • Narad Rampersad
  • Jeffrey Shallit
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)


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.


Automatic Sequence Regular Language Decidable Property Distinct Factor Numeration System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Émilie Charlier
    • 1
  • Narad Rampersad
    • 2
  • Jeffrey Shallit
    • 1
  1. 1.University of WaterlooWaterlooCanada
  2. 2.Department of MathematicsUniversity of LiègeLiègeBelgium

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