Advertisement

Computing the Partial Word Avoidability Indices of Ternary Patterns

  • Francine Blanchet-Sadri
  • Andrew Lohr
  • Shane Scott
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7643)

Abstract

We study pattern avoidance in the context of partial words. The problem of classifying the avoidable unary patterns has been solved, so we move on to binary, ternary, and more general patterns. Our results, which are based on morphisms (iterated or not), determine all the ternary patterns’ avoidability indices or at least give bounds for them.

Keywords

Depth Function Alphabet Size Partial Word Pattern Avoidance Full Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bean, D.R., Ehrenfeucht, A., McNulty, G.: Avoidable patterns in strings of symbols. Pacific Journal of Mathematics 85, 261–294 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Blanchet-Sadri, F.: Algorithmic Combinatorics on Partial Words. Chapman & Hall/CRC Press, Boca Raton, FL (2008)zbMATHGoogle Scholar
  3. 3.
    Blanchet-Sadri, F., Black, K., Zemke, A.: Unary Pattern Avoidance in Partial Words Dense with Holes. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 155–166. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  4. 4.
    Blanchet-Sadri, F., Mercaş, R., Simmons, S., Weissenstein, E.: Avoidable binary patterns in partial words. Acta Informatica 48(1), 25–41 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Blanchet-Sadri, F., Mercaş, R., Simmons, S., Weissenstein, E.: Erratum to: Avoidable binary patterns in partial words. Acta Informatica 49, 53–54 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Cassaigne, J.: Unavoidable binary patterns. Acta Informatica 30, 385–395 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Cassaigne, J.: Motifs évitables et régularités dans les mots. PhD thesis, Paris VI (1994)Google Scholar
  8. 8.
    Clark, R.J.: The existence of a pattern which is 5-avoidable but 4-unavoidable. International Journal of Algebra and Computation 16, 351–367 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Lothaire, M.: Algebraic Combinatorics on Words. Cambridge University Press, Cambridge (2002)zbMATHGoogle Scholar
  10. 10.
    Ochem, P.: A generator of morphisms for infinite words. RAIRO-Theoretical Informatics and Applications 40, 427–441 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Zimin, A.I.: Blocking sets of terms. Mathematics of the USSR-Sbornik 47, 353–364 (1984)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Andrew Lohr
    • 2
  • Shane Scott
    • 3
  1. 1.Department of Computer ScienceUniversity of North CarolinaGreensboroUSA
  2. 2.Department of Mathematics, Mathematics BuildingUniversity of MarylandCollege ParkUSA
  3. 3.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations