Advertisement

On Normal Forms for Networks of Evolutionary Processors

  • Jürgen Dassow
  • Florin Manea
  • Bianca Truthe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6714)

Abstract

In this paper we show that some aspects of networks of evolutionary processors can be normalized or simplified without loosing generative power. More precisely, we show that one can use very small finite automata for the control of the communication. We first prove that the networks with evolutionary processors remain computationally complete if one restricts the control automata to have only one state, but underlying graphs of the networks have no fixed structure and the rules are applied in three different modes. Moreover, we show that networks where the rules are applied arbitrary, and all the automata for control have one state, cannot generate all recursively enumerable languages. Finally, we show that one can generate all recursively enumerable languages by complete networks, where the rules are applied arbitrary, but the automata for control have at most two states.

Keywords

Normal Form Output Node Formal Language Regular Language Communication Step 
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.
    Hillis, W.D.: The Connection Machine. MIT Press, Cambridge (1986)CrossRefGoogle Scholar
  2. 2.
    Errico, L.D., Jesshope, C.: Towards a New Architecture for Symbolic Processing. In: Proc. of AIICSR 1994, pp. 31–40. World Scientific Publishing Co., Inc., River Edge (1994)Google Scholar
  3. 3.
    Fahlman, S.E., Hinton, G.E., Sejnowski, T.J.: Massively Parallel Architectures for AI: NETL, Thistle, and Boltzmann Machines. In: Proc. AAAI 1983, pp. 109–113 (1983)Google Scholar
  4. 4.
    Csuhaj-Varjú, E., Salomaa, A.: Networks of Parallel Language Processors. In: Păun, G., Salomaa, A. (eds.) New Trends in Formal Languages. LNCS, vol. 1218, pp. 299–318. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    Csuhaj-Varjú, E., Mitrana, V.: Evolutionary Systems: A Language Generating Device Inspired by Evolving Communities of Cells. Acta Informatica 36(11), 913–926 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Păun, G.: Computing with Membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Păun, G., Sântean, L.: Parallel Communicating Grammar Systems: The Regular Case. Annals of University of Bucharest, Ser. Matematica-Informatica 38, 55–63 (1989)zbMATHGoogle Scholar
  8. 8.
    Castellanos, J., Martín-Vide, C., Mitrana, V., Sempere, J.M.: Networks of evolutionary processors. Acta Informatica 39(6-7), 517–529 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Sankoff, D., Leduc, G., Antoine, N., Paquin, B., Lang, F., Cedergren, R.: Gene Order Comparisons for Phylogenetic Inference: Evolution of the Mitochondrial Genome. Proc. of the National Academy of Sciences of the United States of America 89(14), 6575–6579 (1992)CrossRefGoogle Scholar
  10. 10.
    Martín-Vide, C., Mitrana, V.: Networks of evolutionary processors: Results and perspectives. In: Molecular Computational Models: Unconventional Approaches, pp. 78–114 (2005)Google Scholar
  11. 11.
    Alhazov, A., Dassow, J., Martín-Vide, C., Rogozhin, Y., Truthe, B.: On networks of evolutionary processors with nodes of two types. Fundamenta Informaticae 91, 1–15 (2009)MathSciNetzbMATHGoogle Scholar
  12. 12.
    Alhazov, A., Csuhaj-Varjú, E., Martín-Vide, C., Rogozhin, Y.: On the size of computationally complete hybrid networks of evolutionary processors. Theoretical Computer Science 410, 3188–3197 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Castellanos, J., Martín-Vide, C., Mitrana, V., Sempere, J.M.: Solving NP-Complete Problems With Networks of Evolutionary Processors. In: Mira, J., Prieto, A.G. (eds.) IWANN 2001. LNCS, vol. 2084, pp. 621–628. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  14. 14.
    Dassow, J., Manea, F., Truthe, B.: A Normal Form for Networks of Evolutionary Processors. Technical report, Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik (2010), http://theo.cs.uni-magdeburg.de/pubs/preprints/pp-afl-2010-02.pdf
  15. 15.
    Rozenberg, G., Salomaa, A.: Handbook of Formal Languages. Springer, Heidelberg (1997)CrossRefzbMATHGoogle Scholar
  16. 16.
    Geffert, V.: Normal forms for phrase-structure grammars. RAIRO – Theoretical Informatics and Applications 25, 473–496 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Dassow, J., Manea, F., Truthe, B.: Networks of Evolutionary Processors with Subregular Filters. Technical report, Otto-von-Guericke-Universität Magdeburg, Fakultät für Informatik (2011), http://theo.cs.uni-magdeburg.de/pubs/preprints/pp-afl-2011-01.pdf
  18. 18.
    Dassow, J., Truthe, B.: On networks of evolutionary processors with filters accepted by two-state-automata (submitted)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jürgen Dassow
    • 1
  • Florin Manea
    • 1
  • Bianca Truthe
    • 1
  1. 1.Fakultät für InformatikOtto-von-Guericke-Universität MagdeburgMagdeburgGermany

Personalised recommendations