Regular Splicing Languages Must Have a Constant

  • Paola Bonizzoni
  • Natasha Jonoska
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6795)


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.


Splice Site Regular Language State Automaton Transitive Component Deterministic Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Berstel, J., Perrin, D.: Theory of Codes. Academic Press Inc., Orlando (1985)zbMATHGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bonizzoni, P., Mauri, G.: Regular splicing languages and subclasses. Theoretical Computer Science 340, 349–363 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bonizzoni, P.: Constants and label-equivalence: A decision procedure for reflexive regular splicing languages. Theoretical Computer Science 411(6), 865–877 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bonizzoni, P., Jonoska, N.: Splicing languages and constants, manuscript (2011)Google Scholar
  7. 7.
    Černý, J.: Poznámka k homogénnym eksperimentom s konecnými automatami. Matematicko-fyzikalny Časopis Slovenskej Akadémie Vied 14, 208–216 (1964)Google Scholar
  8. 8.
    Culik, K., Harju, T.: Splicing semigroups of dominoes and DNA. Discrete Applied Math. 31, 261–277 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Goode, E.: Constants and splicing systems, PHD Thesis, Binghamton University (1999)Google Scholar
  11. 11.
    Goode, E., Pixton, D.: Recognizing splicing languages: Syntactic Monoids and Simultaneous Pumping. Discrete Applied Mathematics 155, 989–1006 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading (2001)zbMATHGoogle Scholar
  14. 14.
    Jonoska, N.: Sofic Systems with Synchronizing Representations. Theoretical Computer Science 158(1-2), 81–115 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lind, D., Marcus, B.: An Introduction to Symbolic Dynamics. Cambridge University Press, New York (1995)CrossRefzbMATHGoogle Scholar
  16. 16.
    Paun, G.: On the splicing operation. Discrete Applied Math. 70, 57–79 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Paun, G., Rozenberg, G., Salomaa, A.: DNA computing, New Computing Paradigms. Springer, Berlin (1998)zbMATHGoogle Scholar
  18. 18.
    Pixton, D.: Regularity of splicing languages. Discrete Applied Math. 69, 101–124 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Schützenberger, M.P.: Sur certaines opérations de fermeture dans le langages rationnels. Symposia Mathematica 15, 245–253 (1975)zbMATHGoogle Scholar
  20. 20.
    Verlan, S.: Head systems and applications to bio-informatics. Ph. D. Thesis, University of Metz (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Paola Bonizzoni
    • 1
  • Natasha Jonoska
    • 2
  1. 1.Dipartimento di Informatica Sistemistica e ComunicazioneUniv. degli Studi di Milano - BicoccaMilanoItaly
  2. 2.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA

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