Acta Informatica

, Volume 48, Issue 1, pp 25–41

Avoidable binary patterns in partial words

  • F. Blanchet-Sadri
  • Robert Mercaş
  • Sean Simmons
  • Eric Weissenstein
Original Article

DOI: 10.1007/s00236-010-0129-0

Cite this article as:
Blanchet-Sadri, F., Mercaş, R., Simmons, S. et al. Acta Informatica (2011) 48: 25. doi:10.1007/s00236-010-0129-0

Abstract

The problem of classifying all the avoidable binary patterns in (full) words has been completely solved (see Chap. 3 of M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, 2002). In this paper, we classify all the avoidable binary patterns in partial words, or sequences that may have some undefined positions called holes. In particular we show that, if we do not substitute any variable of the pattern by a partial word consisting of only one hole, the avoidability index of the pattern remains the same as in the full word case.

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • F. Blanchet-Sadri
    • 1
  • Robert Mercaş
    • 2
  • Sean Simmons
    • 3
  • Eric Weissenstein
    • 4
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.GRLMC, Departament de Filologies RomàniquesUniversitat Rovira i VirgiliTarragonaSpain
  3. 3.Department of MathematicsThe University of Texas at AustinAustinUSA
  4. 4.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA