Skip to main content
SpringerLink
Log in

Algebraic Characterization of the Finite Power Property

  • Conference paper
Automata, Languages and Programming (ICALP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4051))

Included in the following conference series:

  • 1519 Accesses

Abstract

We give a transparent characterization, by means of a certain syntactic semigroup, of regular languages possessing the finite power property. Then we use this characterization to obtain a short elementary proof for the uniform decidability of the finite power property for rational languages in all monoids defined by a confluent regular system of deletion rules. This result in particular covers the case of free groups solved earlier by d’Alessandro and Sakarovitch by means of an involved reduction to the boundedness problem for distance automata.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Berstel, J.: Transductions and Context-Free Languages. Teubner, Stuttgart (1979)

    Google Scholar 

  2. Book, R.V., Otto, F.: String-Rewriting Systems. Springer, New York (1993)

    MATH  Google Scholar 

  3. d’Alessandro, F., Sakarovitch, J.: The finite power property in free groups. Theoret.Comput.Sci. 293(1), 55–82 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hashiguchi, K.: A decision procedure for the order of regular events. Theoret. Comput. Sci. 8(1), 69–72 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hashiguchi, K.: Limitedness theorem on finite automata with distance functions. J. Comput. System Sci. 24, 233–244 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  6. Hashiguchi, K.: Algorithms for determining relative star height and star height. Inform. and Comput. 78(2), 124–169 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  7. Howie, J.M.: Fundamentals of Semigroup Theory. Clarendon Press, Oxford (1995)

    MATH  Google Scholar 

  8. Kirsten, D.: The finite power problem revisited. Inform. Process. Lett. 84(6), 291–294 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kunc, M.: Regular solutions of language inequalities and well quasi-orders. Theoret. Comput. Sci. 348(2-3), 277–293 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Linna, M.: Finite power property of regular languages. In: Nivat, M. (ed.) Automata, Languages and Programming, pp. 87–98. North-Holland, Amsterdam (1973)

    Google Scholar 

  11. Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Berlin (1997)

    MATH  Google Scholar 

  12. Sakarovitch, J.: Easy multiplications. I. The realm of Kleene’s theorem. Inform. and Comput. 74(3), 173–197 (1987)

    MATH  MathSciNet  Google Scholar 

  13. Simon, I.: Limited subsets of a free monoid. In: Proc. 19th Annu. Symp. on Foundations of Computer Science, Piscataway, N.J, pp. 143–150. IEEE, Los Alamitos (1978)

    Google Scholar 

  14. Simon, I.: Recognizable sets with multiplicities in the tropical semiring. In: Koubek, V., Janiga, L., Chytil, M.P. (eds.) MFCS 1988. LNCS, vol. 324, pp. 107–120. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Turku,  

    Michal Kunc

  2. Turku Centre for Computer Science, FIN-20014, Turku, Finland

    Michal Kunc

Authors
  1. Michal Kunc
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università Ca’ Foscari, Venice

    Michele Bugliesi

  2. Interdisciplinary Institute for BroadBand Technology (IBBT), Belgium

    Bart Preneel

  3. ECS, University of Southampton, UK

    Vladimiro Sassone

  4. FB Informatik, Univ. Dortmund, LS2, 44221, Dortmund, Germany

    Ingo Wegener

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kunc, M. (2006). Algebraic Characterization of the Finite Power Property. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_12

Download citation

  • DOI: https://doi.org/10.1007/11786986_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35904-3

  • Online ISBN: 978-3-540-35905-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation