Advertisement

Squareable Words

  • Francine Blanchet-SadriEmail author
  • Abraham Rashin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)

Abstract

For a word w and a partial word u of the same length, say w derives u if w can be transformed into u by inserting holes, i.e., by replacing letters with don’t cares, with the restriction that no two holes may be within distance two. We present and prove a necessary and sufficient condition for a word of even length (at least eight) to not derive any squares (such word is called non-squareable). The condition can be decided in O(n) time, where n is the length of the word.

Keywords

Combinatorics on words Partial words Squareable word Squares 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berstel, J., Boasson, L.: Partial words and a theorem of Fine and Wilf. Theoretical Computer Science 218, 135–141 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Blanchet-Sadri, F.: Algorithmic Combinatorics on Partial Words. Chapman & Hall/CRC Press, Boca Raton (2008)zbMATHGoogle Scholar
  3. 3.
    Blanchet-Sadri, F., Mercaş, R., Rashin, A., Willett, E.: Periodicity algorithms and a conjecture on overlaps in partial words. Theoretical Computer Science 443, 35–45 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Blanchet-Sadri, F., Mercaş, R., Scott, G.: A generalization of Thue freeness for partial words. Theoretical Computer Science 410, 793–800 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Fischer, M., Paterson, M.: String matching and other products. In: Karp, R. (ed.) 7th SIAM-AMS Complexity of Computation, pp. 113–125 (1974)Google Scholar
  6. 6.
    Halava, V., Harju, T., Kärki, T., Séébold, P.: Overlap-freeness in infinite partial words. Theoretical Computer Science 410, 943–948 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Manea, F., Mercaş, R.: Freeness of partial words. Theoretical Computer Science 389, 265–277 (2007)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Thue, A.: Über unendliche Zeichenreihen. Norske Vid. Selsk. Skr. I, Mat. Nat. Kl. Christiana 7, 1–22 (1906). (Reprinted in Selected Mathematical Papers of Axel Thue, T. Nagell, editor, Universitetsforlaget, Oslo, Norway (1977), pp. 139–158)zbMATHGoogle Scholar
  9. 9.
    Thue, A.: Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr. I, Mat. Nat. Kl. Christiana 1, 1–67 (1912). (Reprinted in Selected Mathematical Papers of Axel Thue, T. Nagell, editor, Universitetsforlaget, Oslo, Norway (1977), pp. 413–478)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.Department of MathematicsRutgers UniversityPiscatawayUSA

Personalised recommendations