Skip to main content
SpringerLink
Log in
Book cover

International Conference on Implementation and Application of Automata

CIAA 2015: Implementation and Application of Automata pp 199–210Cite as

Expressive Capacity of Concatenation Freeness

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9223))

Abstract

The expressive capacity of regular expressions without concatenation, but with complementation and a finite set of words as literals is studied. In particular, a characterization of unary concatenation-free languages by the Boolean closure of certain sets of languages is shown. The characterization is then used to derive regular languages that are not concatenation free. Closure properties of the family of concatenation-free languages are derived. Furthermore, the position of the family in the subregular hierarchy is considered and settled for the unary case. In particular, there are concatenation-free languages that do not belong to all of the families in the hierarchy. Moreover, except for comets, all of the families in the subregular hierarchy considered are strictly included in the family of concatenation-free languages.

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 EPUB and 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

References

  1. Brzozowski, J.A.: Canonical regular expressions and minimal state graphs for definite events. In: Mathematical Theory of Automata, pp. 529–561. Polytechnic Institute of Brooklyn (1962)

    Google Scholar 

  2. Brzozowski, J.A.: Roots of star events. J. ACM 14, 466–477 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brzozowski, J.A., Cohen, R.S.: On decompositions of regular events. J. ACM 16, 132–144 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  4. Cohen, R.S., Brzozowski, J.A.: Dot-depth of star-free events. J. Comput. Syst. Sci. 5, 1–16 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  5. Havel, I.M.: The theory of regular events II. Kybernetica 6, 520–544 (1969)

    MathSciNet  Google Scholar 

  6. Holzer, M., Kutrib, M.: The complexity of regular(-like) expressions. Int. J. Found. Comput. Sci. 22, 1533–1548 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Holzer, M., Kutrib, M., Meckel, K.: Nondeterministic state complexity of star-free languages. Theoret. Comput. Sci. 450, 68–80 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kleene, S.C.: Representation of events in nerve nets and finite automata. In: Shannon, C.E., McCarthy, J. (eds.) Automata Studies, pp. 3–42. Princeton University Press, Princeton (1956)

    Google Scholar 

  9. McNaughton, R., Papert, S.: Counter-Free Automata. Research Monographs, vol. 65. MIT Press, Cambridge (1971)

    MATH  Google Scholar 

  10. Perles, M., Rabin, M.O., Shamir, E.: The theory of definite automata. IEEE Trans. Electr. Comput. EC-12, 233–243 (1963)

    Google Scholar 

  11. Salomaa, K., Yu, S.: Alternating finite automata and star-free languages. Theoret. Comput. Sci. 234, 167–176 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  12. Schützenberger, M.P.: On finite monoids having only trivial subgroups. Inform. Control 8, 190–194 (1965)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Martin Kutrib & Matthias Wendlandt

Authors
  1. Martin Kutrib
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Matthias Wendlandt
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin Kutrib .

Editor information

Editors and Affiliations

  1. Umeå University, Umeå, Sweden

    Frank Drewes

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kutrib, M., Wendlandt, M. (2015). Expressive Capacity of Concatenation Freeness. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22360-5_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22359-9

  • Online ISBN: 978-3-319-22360-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation