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On Bispecial Words and Subword Complexity of DOL Sequences *

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Sequences and their Applications

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

Abstract

We study thesubword complexityof a sequence which counts the number of its distinct factors of a given length. Using the technique ofbispecial words, we find an explicit formula for the subword complexity of a wide class of DOL sequences. We also obtain the characterization of bispecial factors and minimalforbidden wordsof that class of sequences.

Supported in part by RFBR (grants 96-01-01800 and 97-01-01075) and Federal Aim Program “Integration” (grant 473)

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References

  1. J.-P. Allouche, Sur la complexité des suitesinfinies Bull. Belg. Math. Soc. 1(1994), 133–143.

    MathSciNet  MATH  Google Scholar 

  2. M.-P. Béai, F. Mignosi, and A. Restivo, Minimal Forbidden Words and Symbolic DynamicsSTACS’96Lect. Notes Comp. Sci.1046(1996) 555–566.

    Article  Google Scholar 

  3. J. Cassaigne, An algorithm to test if a given circular HDOL-language avoids a patternIFIP World Computer Congress’94Elsevier (North-Holland)1(1994), 459–464.

    MathSciNet  Google Scholar 

  4. J. Cassaigne, Motifs évitables et régularités dans les motsThèse de DoctoratUniversité Paris 6 (1994). Rapport LITP TH 94–04.

    Google Scholar 

  5. J. Cassaigne, Complexité et facteurs spéciauxBull. Belg. Math. Soc.4(1997), 67–88.

    MathSciNet  MATH  Google Scholar 

  6. M. Crochemore, F. Mignosi, and A. Restivo, Minimal Forbidden Words and Factor AutomataMFCS’98Lect. Notes Comp. Sci.1450(1998), 665–673.

    Article  MathSciNet  Google Scholar 

  7. S. Ferenczi, Complexity of Sequences and Dynamical SystemsDiscrete Math.206(1999), to appear.

    Google Scholar 

  8. A. Frid, On Uniform DOL WordsSTACS’98Lect. Notes Comp. Sci.1373(1998), 544–554.

    Article  MathSciNet  Google Scholar 

  9. V. Keränen, Abelian Squares are Avoidable on 4 LettersICALP’92Lect. Notes Comp. Sci.623(1992), 41–52.

    Article  Google Scholar 

  10. R. Kolpakov, G. Kucherov, Minimal Letter Frequency in n-th Power-free Binary Words.MFCS’97Lect. Notes Comp. Sci.1295(1997) 347–357.

    Article  MathSciNet  Google Scholar 

  11. M. Lothaire, “Combinatorics on Words”, Addison-Wesley, Reading, Mass., 1983.

    Google Scholar 

  12. F. Mignosi and P. Séébold, If a DOL language is k -power-free then it is circularICALP’93Lect. Notes Comp. Sci.700(1993), 507–518.

    Article  Google Scholar 

  13. B. Mossé, Puissances de mots et reconnaissabilité des points fixes d’une substitutionTheoret.Comput. Sci.99(1992), 327–334.

    Article  MathSciNet  MATH  Google Scholar 

  14. B. Mossé, Reconnaissabilité des substitutions et complexité des suites automatiquesBull. Soc. Math. France 124(1996), 329–346.

    MathSciNet  MATH  Google Scholar 

  15. B. Mossé, On the complexity function of fixed points of substitutions (1996), Unpublished.

    Google Scholar 

  16. J.-J. Pansiot, Complexité des facteurs des mots infinis engendrés par morphismes itérésICALP’84Lect. Notes Comp. Sci.172(1984), 380–389.

    Article  MathSciNet  Google Scholar 

  17. T. Tapsoba, Automates calculant la complexité des suites automatiquesJournal de Théorie des nombres de Bordeaux 6(1994), 127–134.

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Novosibirsk State University, Pirogova st. 2, 630090, Novosibirsk, Russia

    A. Frid & S. V. Avgustinovich

Authors
  1. A. Frid
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  2. S. V. Avgustinovich
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Editor information

Editors and Affiliations

  1. Department of Computer Science, School of Computing, National University of Singapore, Lower Kent Ridge Road, Singapore, 119260

    C. Ding

  2. Department of Informatics, University of Bergen, N-5020, Bergen, Norway

    T. Helleseth

  3. Institute of Information Processing, Austrian Academy of Sciences, Sonnenfelsgasse 19, A01010, Vienna, Austria

    H. Niederreiter

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© 1999 Springer-Verlag London

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Frid, A., Avgustinovich, S.V. (1999). On Bispecial Words and Subword Complexity of DOL Sequences *. In: Ding, C., Helleseth, T., Niederreiter, H. (eds) Sequences and their Applications. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0551-0_13

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  • DOI: https://doi.org/10.1007/978-1-4471-0551-0_13

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-196-2

  • Online ISBN: 978-1-4471-0551-0

  • eBook Packages: Springer Book Archive

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