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Avoidable binary patterns in partial words

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An Erratum to this article was published on 08 December 2011

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.

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References

  1. Bean D.R., Ehrenfeucht A., McNulty G.: Avoidable patterns in strings of symbols. Pac. J. Math. 85, 261–294 (1979)

    MATH  MathSciNet  Google Scholar 

  2. Blanchet-Sadri F.: Algorithmic Combinatorics on Partial Words. Chapman & Hall/CRC Press, Boca Raton (2008)

    MATH  Google Scholar 

  3. Blanchet-Sadri F., Mercaş R., Scott G.: A generalization of Thue freeness for partial words. Theor. Comput. Sci. 410(8–10), 793–800 (2009)

    Article  MATH  Google Scholar 

  4. Blanchet-Sadri, F., Mercaş, R., Simmons, S., Weissenstein, E.: Avoidable binary patterns in partial words. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010, 4th International Conference on Language and Automata Theory and Applications, Trier, Germany, Lecture Notes in Computer Science, vol. 6031, pp. 106–117. Springer, Berlin (2010)

  5. Cassaigne J.: Unavoidable binary patterns. Acta Informatica 30, 385–395 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  6. Halava V., Harju T., Kärki T., Séébold P.: Overlap-freeness in infinite partial words. Theor. Comput. Sci. {\bf 410acute;(8–10), 943–948 (2009)

    Article  MATH  Google Scholar 

  7. Lothaire M.: Combinatorics on Words. Cambridge University Press, Cambridge (1997)

    Book  MATH  Google Scholar 

  8. Lothaire M.: Algebraic Combinatorics on Words. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  9. Manea F., Mercaş R.: Freeness of partial words. Theor. Comput. Sci. 389(1–2), 265–277 (2007)

    MATH  Google Scholar 

  10. Roth P.: Every binary pattern of length six is avoidable on the two-letter alphabet. Acta Informatica 29, 95–106 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  11. Schmidt, U.: Motifs inévitables dans les mots. Technical Report LITP 86–63 Thèse Paris VI (1986)

  12. Schmidt U.: Avoidable patterns on two letters. Theor. Comput. Sci. 63, 1–17 (1989)

    Article  MATH  Google Scholar 

  13. 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, T., Nagell, T. (eds.) pp. 139–158. Universitetsforlaget, Oslo, Norway (1977))

  14. 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, T., Nagell, T. (eds) pp. 413–478. Universitetsforlaget, Oslo, Norway (1977))

  15. Zimin A.I.: Blocking sets of terms. Mathematics of the USSR-Sbornik 47(2), 353–364 (1984)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of North Carolina, P.O. Box 26170, Greensboro, NC, 27402–6170, USA

    F. Blanchet-Sadri

  2. GRLMC, Departament de Filologies Romàniques, Universitat Rovira i Virgili, Av. Catalunya 35, Tarragona, 43002, Spain

    Robert Mercaş

  3. Department of Mathematics, The University of Texas at Austin, 2515 Speedway Rm 8, Austin, TX, 78712–0233, USA

    Sean Simmons

  4. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Amos Eaton 301, 110 8th Street, Troy, NY, 12180, USA

    Eric Weissenstein

Authors
  1. F. Blanchet-Sadri
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  2. Robert Mercaş
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  3. Sean Simmons
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  4. Eric Weissenstein
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Corresponding author

Correspondence to F. Blanchet-Sadri.

Additional information

This material is based upon work supported by the National Science Foundation under Grant No. DMS–0754154. The Department of Defense is also gratefully acknowledged. Part of this paper was presented at LATA 2010 [4]. We thank the referees of some preliminary versions of this paper for their very valuable comments and/or suggestions. A World Wide Web server interface has been established at http://www.uncg.edu/cmp/research/unavoidablesets4 for automated use of the program. Robert Mercaş’s work was partially supported by Research Grant No. 1323 U07 E30 N-2008/InvAct/Bel, G./BJ01 and Research Grant No. 1355 U07 E30 N-2010PFR-URV-B2-02 of the University Rovira i Virgili.

An erratum to this article can be found at http://dx.doi.org/10.1007/s00236-011-0149-4

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Blanchet-Sadri, F., Mercaş, R., Simmons, S. et al. Avoidable binary patterns in partial words. Acta Informatica 48, 25–41 (2011). https://doi.org/10.1007/s00236-010-0129-0

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