How Many Holes Can an Unbordered Partial Word Contain?

  • Francine Blanchet-Sadri
  • Emily Allen
  • Cameron Byrum
  • Robert Mercaş
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5457)

Abstract

Partial words are sequences over a finite alphabet that may have some undefined positions, or “holes,” that are denoted by \(\ensuremath{\diamond}\)’s. A nonempty partial word is called bordered if one of its proper prefixes is compatible with one of its suffixes (here \(\ensuremath{\diamond}\) is compatible with every letter in the alphabet); it is called unbordered otherwise. In this paper, we investigate the problem of computing the maximum number of holes a partial word of a fixed length can have and still fail to be bordered.

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)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Blanchet-Sadri, F.: Algorithmic Combinatorics on Partial Words. Chapman & Hall/CRC Press (2007)Google Scholar
  3. 3.
    Blanchet-Sadri, F.: Primitive partial words. Discrete Applied Mathematics 148, 195–213 (2005)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Blanchet-Sadri, F., Davis, C., Dodge, J., Mercaş, R., Moorefield, M.: Unbordered partial words. Discrete Applied Mathematics (2008), doi:10.1016/j.dam.2008.04.004Google Scholar
  5. 5.
    Blanchet-Sadri, F.: Open problems on partial words. In: Bel-Enguix, G., Jiménez-López, M., Martín-Vide, C. (eds.) New Developments in Formal Languages and Applications, pp. 11–58. Springer, Berlin (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Emily Allen
    • 2
  • Cameron Byrum
    • 3
  • Robert Mercaş
    • 4
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA
  3. 3.Department of MathematicsUniversity of MississippiUSA
  4. 4.GRLMCUniversitat Rovira i VirgiliTarragonaSpain

Personalised recommendations