Skip to main content

Reduced Languages as ω-Generators

  • Conference paper
Developments in Language Theory (DLT 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4588))

Included in the following conference series:

  • 397 Accesses

Abstract

We consider the following decision problem: “Is a rational ω-language generated by a code ?” Since 1994, the codes admit a in terms of infinite words. We derive from this result the definition of a new class of languages, the reduced languages. A code is a reduced language but the converse does not hold. The idea is to “reduce” easy-to-obtain minimal ω-generators in order to obtain codes as ω-generators.

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

Access this chapter

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. Augros, X.: Etude des générateurs de langages de mots infinis. Master’s thesis, Univ. de Nice - Sophia Antipolis (june 1997)

    Google Scholar 

  2. Berstel, J., Perrin, D.: Theory of codes. Academic Press, London (1985)

    MATH  Google Scholar 

  3. Boasson, L., Nivat, M.: Adherences of languages. Journal of Computer and System Sciences 20, 285–309 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  4. Büchi, J.R.: On a decision method in restricted second order arithmetics. In: International Congress on Logic, Methodology and Philosophy of Science, pp. 1–11. Stanford University Press (1960)

    Google Scholar 

  5. Devolder, J.: Generators with bounded deciphering delay for rational ω-languages. Journal of Automata, Languages and Combinatorics 4(3), 183–204 (1999)

    MATH  MathSciNet  Google Scholar 

  6. Devolder, J., Latteux, M., Litovsky, I., Staiger, L.: Codes and infinite words. Acta. Cybernetica 11(4), 241–256 (1994)

    MATH  MathSciNet  Google Scholar 

  7. Julia, S.: Sur les codes et les ω-codes générateurs de langages de mots infinis. PhD thesis, Université de Nice - Sophia Antipolis (1996)

    Google Scholar 

  8. Julia, S.: A characteristic language for rational ω-powers. In: Proc. 3rd Int. Conf. Developments in Language Theory, pp. 299–308, Thessaloniki (1997)

    Google Scholar 

  9. Julia, S., Litovsky, I., Patrou, B.: On codes, ω-codes and ω-generators. Information Processing Letters 60(1), 1–5 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  10. Karhumäki, J.: On three-element codes. Theoret. Comput. Sc. 40, 3–11 (1985)

    MATH  Google Scholar 

  11. Latteux, M., Timmerman, E.: Finitely generated ω-langages. Information Processing Letters 23, 171–175 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  12. Litovsky, I.: Free submonoids and minimal ω-generators of R ω. Acta. Cybernetica 10(1-2), 35–43 (1991)

    MATH  MathSciNet  Google Scholar 

  13. Litovsky, I.: Prefix-free languages as ω-generators. Information Processing Letters 37, 61–65 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  14. Litovsky, I., Timmerman, E.: On generators of rational ω-power languages. Theoretical Computer Science 53, 187–200 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  15. Lothaire, M.: Algebraic Combinatorics on Words. Cambridge (2002)

    Google Scholar 

  16. Perrin, D., Pin, J.E.: Infinite words. Elsevier Academic Press, Amsterdam (2004)

    MATH  Google Scholar 

  17. Staiger, L.: On infinitary finite length codes. Theoretical Informatics and Applications 20(4), 483–494 (1986)

    MATH  MathSciNet  Google Scholar 

  18. Thomas, W.: Automata on infinite objects. In: Handbook of Theoretical Computer Science, vol. B, ch. 4, Elsevier Science Publishers, Amsterdam (1990)

    Google Scholar 

  19. Tran Vinh Duc. A la recherche des codes générateurs de langages de mots infinis. Master’s thesis, IFI Hanoï - Univ. de Nice - Sophia Antipolis (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Tero Harju Juhani Karhumäki Arto Lepistö

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Julia, S., Duc, T.V. (2007). Reduced Languages as ω-Generators. In: Harju, T., Karhumäki, J., Lepistö, A. (eds) Developments in Language Theory. DLT 2007. Lecture Notes in Computer Science, vol 4588. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73208-2_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73208-2_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73207-5

  • Online ISBN: 978-3-540-73208-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics