Enumeration and Decidable Properties of Automatic Sequences

  • Émilie Charlier
  • Narad Rampersad
  • Jeffrey Shallit
Conference paper

DOI: 10.1007/978-3-642-22321-1_15

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)
Cite this paper as:
Charlier É., Rampersad N., Shallit J. (2011) Enumeration and Decidable Properties of Automatic Sequences. In: Mauri G., Leporati A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg

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.

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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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