Skip to main content
SpringerLink
Log in
Book cover

Formal and Natural Computing pp 69–76Cite as

The Branching Point Approach to Conway’s Problem

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2300))

Abstract

A word u is a branching point for a set of words X if there are two different letters a and b such that both ua and ub can be extended to words in X +. A branching point u is critical for X if u ∉ X +. Using these notions, we give an elementary solution for Conway’s Problem in the case of finite biprefixes. We also discuss a possible extension of this approach towards a complete solution for Conway’s Problem.

Supported by the Academy of Finland under grant 44087

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Bergman, Centralizers in Free Associative Algebras, Transactions of the American Mathematical Society 137: 327–344, 1969.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Berstel, D. Perrin, Theory of Codes, Academic Press, New York, 1985.

    MATH  Google Scholar 

  3. C. Choffrut, J. Karhumäki, Combinatorics onWords. In G. Rozenberg, A. Salomaa (Eds.), Handbook of Formal Languages, vol. 1: 329–438, Springer-Verlag, 1997.

    Google Scholar 

  4. C. Choffrut, J. Karhumäki, N. Ollinger, The Commutation of Finite Sets: A Challenging Problem, Theoret. Comput. Sci., to appear.

    Google Scholar 

  5. P.M. Cohn, Centralisateurs dans les corps libres, in J. Berstel (Ed.), Séries formelles: 45–54, Paris, 1978.

    Google Scholar 

  6. J.H. Conway, Regular Algebra and Finite Machines, Chapman Hall, 1971.

    Google Scholar 

  7. T. Harju, I. Petre, On Commutation and Primitive Roots of Codes, Submitted.

    Google Scholar 

  8. J. Karhumäki, Challenges of Commutation: An Advertisement, in Proc. of FCT 2001, LNCS 2138, 15–23, Springer, 2001.

    Google Scholar 

  9. J. Karhumäki, I. Petre, Conway’s Problem for Three Word Sets, Theoret. Comput. Sci., to appear; preliminary version in Proc. ICALP 2000, LNCS 1853 536–546, Springer, 2000.

    Google Scholar 

  10. J. Karhumäki, I. Petre, Conway’s Problem and the Commutation of Languages, Bulletin of EATCS 74, 171–177, 2001.

    MATH  Google Scholar 

  11. M. Lothaire, Combinatorics on Words, Addison-Wesley, Reading, MA., 1983.

    MATH  Google Scholar 

  12. M. Lothaire, Algebraic Combinatorics on Words, Cambridge University Press, to appear.

    Google Scholar 

  13. A. Mateescu, A. Salomaa, S. Yu, On the Decomposition of Finite Languages, TUCS Technical Report 222, http://www.tucs/, 1998.

  14. D. Perrin, Codes Conjugués, Information and Control 20: 222–231, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  15. B. Ratoandromanana, Codes et Motifs, RAIRO Inform. Theor., 23(4): 425–444, 1989.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Turku and Turku Centre for Computer Science (TUCS), 20014, Turku, Finland

    Juhani Karhumäki & Ion Petre

Authors
  1. Juhani Karhumäki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ion Petre
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Computer Science Department, Technical University of Munich, Arcisstraße 21, 80333, Munich, Germany

    Wilfried Brauer

  2. Computer Science Department, Technical University of Berlin, Franklinstraße 28/29, 10587, Berlin, Germany

    Hartmut Ehrig

  3. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  4. Turku Centre for Computer Science, Lemminkäisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Karhumäki, J., Petre, I. (2002). The Branching Point Approach to Conway’s Problem. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds) Formal and Natural Computing. Lecture Notes in Computer Science, vol 2300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45711-9_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-45711-9_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43190-9

  • Online ISBN: 978-3-540-45711-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation