How Many Holes Can an Unbordered Partial Word Contain?

  • Francine Blanchet-Sadri
  • Emily Allen
  • Cameron Byrum
  • Robert Mercaş
Conference paper

DOI: 10.1007/978-3-642-00982-2_15

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5457)
Cite this paper as:
Blanchet-Sadri F., Allen E., Byrum C., Mercaş R. (2009) How Many Holes Can an Unbordered Partial Word Contain?. In: Dediu A.H., Ionescu A.M., Martín-Vide C. (eds) Language and Automata Theory and Applications. LATA 2009. Lecture Notes in Computer Science, vol 5457. Springer, Berlin, Heidelberg

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.

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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

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