Advertisement

An Answer to a Conjecture on Overlaps in Partial Words Using Periodicity Algorithms

  • Francine Blanchet-Sadri
  • Robert Mercaş
  • Abraham Rashin
  • Elara Willett
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5457)

Abstract

We propose an algorithm that given as input a full word w of length n, and positive integers p and d, outputs (if any exists) a maximal p-periodic partial word contained in w with the property that no two holes are within distance d. Our algorithm runs in O(nd) time and is used for the study of freeness of partial words. Furthermore, we construct an infinite word over a five-letter alphabet that is overlap-free even after the insertion of an arbitrary number of holes, answering affirmatively a conjecture from Blanchet-Sadri, Mercaş, and Scott.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Manea, F., Mercaş, R.: Freeness of partial words. Theoretical Computer Science 389, 265–277 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blanchet-Sadri, F., Mercaş, R., Scott, G.: A generalization of Thue freeness for partial words. Theoretical Computer Science (2008), doi:10.1016/j.tcs.2008.11.006Google Scholar
  3. 3.
    Thue, A.: Uber unendliche Zeichenreihen. Norske Vid. Selsk. Skr. I, Mat. Nat. Kl. Christiana 7, 1–22 (1906)zbMATHGoogle Scholar
  4. 4.
    Thue, A.: Uber die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr. I, Mat. Nat. Kl. Christiana 1, 1–67 (1912)zbMATHGoogle Scholar
  5. 5.
    Halava, V., Harju, T., Kärki, T.: Overlap-freeness in infinite partial words. Technical Report 888, Turku Centre for Computer Science (2008)Google Scholar
  6. 6.
    Lothaire, M.: Combinatorics on Words. Cambridge University Press, Cambridge (1997)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Robert Mercaş
    • 2
  • Abraham Rashin
    • 3
  • Elara Willett
    • 4
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.GRLMCUniversitat Rovira i VirgiliTarragonaSpain
  3. 3.Department of MathematicsRutgers UniversityPiscatawayUSA
  4. 4.Department of MathematicsOberlin CollegeOberlinUSA

Personalised recommendations