Advertisement

Extended Watson-Crick L Systems with Regular Trigger Languages

  • David Sears
  • Kai Salomaa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6714)

Abstract

Watson-Crick Lindenmayer systems (L systems) add a control mechanism to ordinary L system derivations. The mechanism is inspired by the complementarity relation in DNA strings, and it is formally defined in terms of a trigger language (trigger, for short). In this paper we prove that Uni-Transitional Watson-Crick E0L systems with regular triggers can recognize the recursively enumerable (RE) languages. We also find that even if the trigger is nondeterministically applied and the number of its applications can be unbounded then the computational power does not change. In the case where the number of applications of the trigger is bounded we find that the computational power lies within the ET0L languages. We also find that Watson-Crick ET0L systems where the number of complementary transitions is bounded by any natural number are equivalent in expressive power.

Keywords

Derivation Step Deterministic Finite Automaton Derivation Mode Complementary Transition Valid Simulation 
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.
    Adleman, L.M.: Molecular Computation Of Solutions To Combinatorial Problems. Science 266, 1021–1024 (1994)CrossRefGoogle Scholar
  2. 2.
    Bar-Hillel, Y., Perles, M., Shamir, E.: On Formal Properties of Simple Phrase-Structure Grammars. Zeitschrift für Phonetik, Sprachwissenschaft und Kommunikationsforschung 14, 143–177 (1961)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Csima, J., Csuhaj-Varjú, E., Salomaa, A.: Power and size of extended Watson-Crick L systems. Theor. Comput. Sci. 290(3), 1665–1678 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Csuhaj-Varjú, E.: Computing by networks of Watson-Crick D0L systems. In: Ito, M. (ed.) Algebraic Systems, Formal Languages and Computation. RIMS Kokyroku 1166, Research Institute for Mathematical Sciences, pp. 43–51. Kyoto University, Kyoto (August 2000)Google Scholar
  5. 5.
    Honkala, J., Salomaa, A.: Watson-Crick D0L systems with regular triggers. Theor. Comput. Sci. 259(1-2), 689–698 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Mihalache, V., Salomaa, A.: Lindenmayer and DNA: Watson-Crick D0L Systems. Bulletin of the EATCS 62 (1997)Google Scholar
  7. 7.
    Mihalache, V., Salomaa, A.: Language-Theoretic Aspects of DNA Complementarity. Theor. Comput. Sci. 250(1-2), 163–178 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Penttonen, M.: One-Sided and Two-Sided Context in Formal Grammars. Information and Control 25(4), 371–392 (1974)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Rozenberg, G., Salomaa, A.: The Mathematical Theory of L systems. Academic Press, New York (1980)zbMATHGoogle Scholar
  10. 10.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Word, Language, Grammar, vol. 1. Springer-Verlag New York, Inc., New York (1997)zbMATHGoogle Scholar
  11. 11.
    Salomaa, A.: Turing, Watson-Crick And Lindenmayer. Aspects Of DNA Complementarity. In: Calude, C., Casti, J., Dinneen, M.J. (eds.) Unconventional Models of Computation, pp. 94–107. Springer, Heidelberg (1997)Google Scholar
  12. 12.
    Salomaa, A.: Watson-Crick Walks and Roads on D0L Graphs. Acta Cybern 14(1), 179–192 (1999)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Salomaa, A.: Uni-transitional Watson-Crick D0L systems. Theor. Comput. Sci. 281(1-2), 537–553 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Sears, D.: The Computational Power of Extended Watson-Crick L Systems. Master’s thesis, School of Computing, Queen’s University, Kingston, Ontario, Canada (2010), http://hdl.handle.net/1974/6224
  15. 15.
    Sosík, P.: D0L System + Watson-Crick Complementarity = Universal Computation. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 308–320. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Sosík, P.: Universal computation with Watson-Crick D0L systems. Theor. Comput. Sci. 289(1), 485–501 (2002)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • David Sears
    • 1
  • Kai Salomaa
    • 1
  1. 1.School of ComputingQueen’s UniversityKingstonCanada

Personalised recommendations