Computationally Complete Spiking Neural P Systems without Delay: Two Types of Neurons Are Enough

  • Rudolf Freund
  • Marian Kogler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6501)


In this paper, we consider spiking neural P systems without delay with specific restrictions on the types of neurons. Two neurons are considered to be of the same type if the rules, the number of spikes in the initial configuration and the number of outgoing synapses are identical. We show that computational completeness can be achieved in both the generating and the accepting case with only two types of neurons, where the number of neurons with unbounded rules is constant even minimal.


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  1. 1.
    García-Arnau, M., Peréz, D., Rodríguez-Patón, A., Sosík, P.: Spiking neural P systems: Stronger normal forms. In: Gutiérrez-Naranjo, M.A., Păun, G., Romero-Jiménez, A., Riscos-Núñez, A. (eds.) Proceedings of the Fifth Brainstorming Week on Membrane Computing, pp. 33–62 (2007)Google Scholar
  2. 2.
    Ibarra, O.H., Păun, A., Păun, G., Rodríguez-Patón, A., Sosík, P., Woodworth, S.: Normal forms for spiking neural P systems. Theor. Comput. Sci. 372(2-3), 196–217 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Ionescu, M., Păun, G., Yokomori, T.: Spiking neural P systems. Fundam. Inf. 71(2,3), 279–308 (2006)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall, Inc., Upper Saddle River (1967)zbMATHGoogle Scholar
  5. 5.
    Pan, L., Păun, G.: Spiking neural P systems: An improved normal form. Theoretical Computer Science 411(6), 906–918 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Păun, A., Păun, G.: Small universal spiking neural P systems. Biosystems 90(1), 48–60 (2007)CrossRefzbMATHGoogle Scholar
  7. 7.
    Păun, G.: Computing with membranes. J. of Computer and System Sci. 61(1), 108–143 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Păun, G.: Membrane Computing: An Introduction. Springer, New York (2002)CrossRefzbMATHGoogle Scholar
  9. 9.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Word, Language, Grammar, vol. 1. Springer, Heidelberg (1997)zbMATHGoogle Scholar
  10. 10.
    Zeng, X., Zhang, X., Pan, L.: Homogeneous spiking neural P systems. Fundam. Inf. 97(1-2), 275–294 (2009)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Zhang, X., Zeng, X., Pan, L.: Smaller universal spiking neural P systems. Fundam. Inf. 87(1), 117–136 (2008)MathSciNetzbMATHGoogle Scholar
  12. 12.
    The P Systems Web Page,

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Rudolf Freund
    • 1
  • Marian Kogler
    • 1
    • 2
  1. 1.Faculty of InformaticsVienna University of TechnologyViennaAustria
  2. 2.Institute of Computer ScienceMartin Luther University Halle-WittenbergHalle (Saale)Germany

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