Skip to main content
SpringerLink
Log in

Two-Sided Bounds for the Growth Rates of Power-Free Languages

  • Conference paper
Developments in Language Theory (DLT 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5583))

Included in the following conference series:

Abstract

The growth properties of power-free languages over finite alphabets are studied. A method to obtain sharp two-sided bounds of the growth rate of β-power-free languages for arbitrary rational number β ≥ 2 is obtained. A table of the growth rates, calculated with the absolute error less than 10− 5 for different particular power-free languages, is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bell, J.P., Goh, T.L.: Exponential lower bounds for the number of words of uniform length avoiding a pattern. Information and Computation 205, 1295–1306 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Berstel, J.: Growth of repetition-free words – a review. Theor. Comput. Sci. 340, 280–290 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Berstel, J., Karhumäki, J.: Combinatorics on words: A tutorial. Bull. Eur. Assoc. Theor. Comput. Sci. 79, 178–228 (2003)

    MathSciNet  MATH  Google Scholar 

  4. Brandenburg, F.-J.: Uniformly growing k-th power free homomorphisms. Theor. Comput. Sci. 23, 69–82 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  5. Crochemore, M., Mignosi, F., Restivo, A.: Automata and forbidden words. Inform. Processing Letters 67(3), 111–117 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cvetković, D.M., Doob, M., Sachs, H.: Spectra of graphs, 3rd edn. Theory and applications. Johann Ambrosius Barth, Heidelberg (1995)

    MATH  Google Scholar 

  7. Gantmacher, F.R.: Application of the theory of matrices. Interscience, New York (1959)

    MATH  Google Scholar 

  8. Karhumäki, J., Shallit, J.: Polynomial versus exponential growth in repetition-free binary words. J. Combin. Theory. Ser. A 105, 335–347 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kobayashi, Y.: Repetition-free words. Theor. Comp. Sci. 44, 175–197 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kolpakov, R.: On the number of repetition-free words. In: Electronic proceedings of Workshop on words and automata (WOWA 2006), S.-Petersburg, #6 (2006)

    Google Scholar 

  11. Lothaire, M.: Combinatorics on words. Addison-Wesley, Reading (1983)

    MATH  Google Scholar 

  12. Ochem, P., Reix, T.: Upper bound on the number of ternary square-free words. In: Electronic proceedings of Workshop on words and automata (WOWA’06), S.-Petersburg, #8 (2006)

    Google Scholar 

  13. Restivo, A., Salemi, S.: Overlap-free words on two symbols. In: Perrin, D., Nivat, M. (eds.) Automata on Infinite Words. LNCS, vol. 192, pp. 196–206. Springer, Heidelberg (1985)

    Chapter  Google Scholar 

  14. Shur, A.M.: Comparing complexity functions of a language and its extendable part. RAIRO Theor. Inf. Appl. 42, 647–655 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Shur, A.M.: Growth rates of complexity of power-free languages. Submitted to Theor. Comp. Sci (2008)

    Google Scholar 

  16. Shur, A.M.: Combinatorial complexity of regular languages. In: Hirsch, E.A., Razborov, A.A., Semenov, A., Slissenko, A. (eds.) Computer Science – Theory and Applications. LNCS, vol. 5010, pp. 289–301. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  17. Thue, A.: Über unendliche Zeichenreihen, Kra. Vidensk. Selsk. Skrifter. I. Mat.-Nat. Kl., Christiana 7, 1–22 (1906)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ural State University, Russia

    Arseny M. Shur

Authors
  1. Arseny M. Shur
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Formale Methoden der Informatik, FMI, Universität Stuttgart, Universitätsstrasse 38, 70569, Stuttgart, Germany

    Volker Diekert  & Dirk Nowotka  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Shur, A.M. (2009). Two-Sided Bounds for the Growth Rates of Power-Free Languages. In: Diekert, V., Nowotka, D. (eds) Developments in Language Theory. DLT 2009. Lecture Notes in Computer Science, vol 5583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02737-6_38

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02737-6_38

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02736-9

  • Online ISBN: 978-3-642-02737-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation