Skip to main content
Springer Nature Link
Log in

Regular Splicing Languages Must Have a Constant

  • Conference paper
Developments in Language Theory (DLT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6795))

Included in the following conference series:

Abstract

In spite of wide investigations of finite splicing systems in formal language theory, basic questions, such as their characterization, remain unsolved. In search for understanding the class of finite splicing systems, it has been conjectured that a necessary condition for a regular language L to be a splicing language is that L must have a constant in the Schützenberger’s sense. We prove this longstanding conjecture to be true. The result is based on properties of strongly connected components of the minimal deterministic finite state automaton for a regular splicing language.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. Berstel, J., Perrin, D.: Theory of Codes. Academic Press Inc., Orlando (1985)

    MATH  Google Scholar 

  2. Bonizzoni, P., De Felice, C., Mauri, G., Zizza, R.: Regular Languages Generated by Reflexive Finite Linear Splicing Systems. In: Ésik, Z., Fülöp, Z. (eds.) DLT 2003. LNCS, vol. 2710, pp. 134–145. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Bonizzoni, P., De Felice, C., Zizza, R.: The structure of reflexive regular splicing languages via Schützenberger constants. Theoretical Computer Science 334(1-3), 71–98 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bonizzoni, P., Mauri, G.: Regular splicing languages and subclasses. Theoretical Computer Science 340, 349–363 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bonizzoni, P.: Constants and label-equivalence: A decision procedure for reflexive regular splicing languages. Theoretical Computer Science 411(6), 865–877 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Bonizzoni, P., Jonoska, N.: Splicing languages and constants, manuscript (2011)

    Google Scholar 

  7. Černý, J.: Poznámka k homogénnym eksperimentom s konecnými automatami. Matematicko-fyzikalny Časopis Slovenskej Akadémie Vied 14, 208–216 (1964)

    Google Scholar 

  8. Culik, K., Harju, T.: Splicing semigroups of dominoes and DNA. Discrete Applied Math. 31, 261–277 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  9. De Luca, A., Restivo, A.: A characterization of strictly locally testable languages and its application to semigroups of free semigroup. Information and Control 44, 300–319 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  10. Goode, E.: Constants and splicing systems, PHD Thesis, Binghamton University (1999)

    Google Scholar 

  11. Goode, E., Pixton, D.: Recognizing splicing languages: Syntactic Monoids and Simultaneous Pumping. Discrete Applied Mathematics 155, 989–1006 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Head, T.: Formal Language Theory and DNA: an analysis of the generative capacity of specific recombinant behaviours. Bull. Math. Biol. 49, 737–759 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  13. Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (2001)

    MATH  Google Scholar 

  14. Jonoska, N.: Sofic Systems with Synchronizing Representations. Theoretical Computer Science 158(1-2), 81–115 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics. Cambridge University Press, New York (1995)

    Book  MATH  Google Scholar 

  16. Paun, G.: On the splicing operation. Discrete Applied Math. 70, 57–79 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  17. Paun, G., Rozenberg, G., Salomaa, A.: DNA computing, New Computing Paradigms. Springer, Berlin (1998)

    MATH  Google Scholar 

  18. Pixton, D.: Regularity of splicing languages. Discrete Applied Math. 69, 101–124 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  19. Schützenberger, M.P.: Sur certaines opérations de fermeture dans le langages rationnels. Symposia Mathematica 15, 245–253 (1975)

    MATH  Google Scholar 

  20. Verlan, S.: Head systems and applications to bio-informatics. Ph. D. Thesis, University of Metz (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica Sistemistica e Comunicazione, Univ. degli Studi di Milano - Bicocca, Viale Sarca 336, 20126, Milano, Italy

    Paola Bonizzoni

  2. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, USA

    Natasha Jonoska

Authors
  1. Paola Bonizzoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Natasha Jonoska
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Viale Sarca 336, Edificio U14, 20126, Milano, Italy

    Giancarlo Mauri  & Alberto Leporati  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bonizzoni, P., Jonoska, N. (2011). Regular Splicing Languages Must Have a Constant. In: Mauri, G., Leporati, A. (eds) Developments in Language Theory. DLT 2011. Lecture Notes in Computer Science, vol 6795. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22321-1_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22321-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22320-4

  • Online ISBN: 978-3-642-22321-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics