Advertisement

Splicing Normalization and Regularity

  • Vincenzo Manca
Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

Abstract

Some canonic forms of splicing derivations are introduced and the notion of ω-splicing is used for proving that H systems with a finite number of splicing rules and a regular set of axioms generate regular languages.

Keywords

Regular Language Discrete Apply Mathematic Formal Language Theory Linear Derivation Splice System 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L. Adleman, Molecular computation of solutions to combinatorial problems, Science, 266 (Nov. 1994), 1021–1024.CrossRefGoogle Scholar
  2. [2]
    K. Culik II, T. Harju, The regularity of splicing systems and DNA, in Proc. ICALP 1989, Lecture Notes in Computer Science, 372, Springer- Verlag, 1989, 222–233.MathSciNetCrossRefGoogle Scholar
  3. [3]
    K. Culik II, T. Harju, Splicing semigroups of dominoes and DNA, Discrete Applied Mathematics, 31 (1991), 261–277.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    A. De Luca, A. Restivo, A characterization of strictly locally testable languages and its application to subsemigroups of a free semigroup, Information and Control, 44 (1980), 300–319.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    T. Head, Formal language theory and DNA: an analysis of the generative capacity of recombinant behaviors, Bulletin of Mathematical Biology 49 (1987), 737–759.MathSciNetMATHGoogle Scholar
  6. [6]
    T. Head, Splicing schemes and DNA, in: Lindenmayer Systems: Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology, (G. Rozenberg, A. Salomaa, eds.), Springer- Verlag, Berlin, Heidelberg, 1992, 371–383.Google Scholar
  7. [7]
    T. Head, Gh. Păun, D. Pixton, Language theory and molecular genetics, Chapter 7 in Handbook of Language Theory (G. Rozenberg, A. Salomaa, eds.), vol 2, Springer-Verlag, Berlin, Heidelberg, 1997, 295–360.Google Scholar
  8. [8]
    T. Head, Splicing representations of strictly locally testable languages, Discrete Applied Mathematics, 87, 1–3 (1998), 139–147.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    S. C. Kleene, Representation of events in nerve nets and finite automata, in Automata Studies, Princeton Univ. Press, Princeton, NJ, 1956.Google Scholar
  10. [10]
    A. Lindenmayer, Mathematical models for cellular interaction in development, I and II, J. Theoret. Biol., 18 (1968), 280–315.CrossRefGoogle Scholar
  11. [11]
    R. Lipton, DNA solution of hard computational problems, Science, 268 (April 1995), 542–545.CrossRefGoogle Scholar
  12. [12]
    V. Manca, Gh. Păun, Arithmetically controlled H systems, Computer Science Journal of Moldova, 6, 2(17) (1998), 103–118.MATHGoogle Scholar
  13. [13]
    V. Manca, Logical string rewriting, Theoretical Computer Science, to appear.Google Scholar
  14. [14]
    R. McNaughton, S. Papert, Counter-Free Automata, MIT Press, Cambridge, MA, 1971.MATHGoogle Scholar
  15. [15]
    Gh. Păun, On the splicing operation, Discrete Applied Mathematics, 70, 1 (1996), 57–79.MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    Gh. Păun, G. Rozenberg, A. Salomaa, DNA Computing. New Computing Paradigms, Springer-Verlag, Berlin, 1998.MATHGoogle Scholar
  17. [17]
    D. Pixton, Regularity of splicing languages, Discrete Applied Mathematics, 69, 1–2 (1996), 101–124.MathSciNetMATHCrossRefGoogle Scholar
  18. [18]
    D. Pixton, Splicing in abstract families of languages, Technical Report 26/97 of SUNY, Univ. of Binghamton, New York, 1997.Google Scholar
  19. [19]
    G. Rozenberg, A. Salomaa, eds., Handbook of Language Theory, 3 Volumes., Springer-Verlag, Berlin, Heidelberg, 1997.Google Scholar
  20. [20]
    M. P. Schützenberger, Sur certaines operations de fermeture dans les languages rationels, Sympos. Math., 15 (1975), 245–253.Google Scholar

Copyright information

© Springer-Verlag London Limited 2000

Authors and Affiliations

  • Vincenzo Manca
    • 1
  1. 1.Dipartimento di Informatica Corso ItaliaUniversità di PisaPisaItaly

Personalised recommendations