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A Boundary between Universality and Non-universality in Extended Spiking Neural P Systems

  • Turlough Neary
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6031)

Abstract

We solve the problem of finding the smallest possible universal spiking neural P system with extended rules. We give a universal spiking neural P system with extended rules and only 4 neurons. This is the smallest possible universal system of its kind. We prove this by showing that the set of problems solved by spiking neural P systems with 3 neurons is bounded above by NL, and so there exists no such universal system with 3 neurons (for any reasonable definition of universality). Finally, we show that if we generalise the output technique we can give a universal spiking neural P system with extended rules that has only 3 neurons. This is also the smallest possible universal system of its kind.

Keywords

Regular Expression Output Neuron Input Neuron Single Spike Universal 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.

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References

  1. 1.
    Ionescu, M., Păun, G., Yokomori, T.: Spiking neural P systems. Fundamenta Informaticae 71(2-3), 279–308 (2006)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Korec, I.: Small universal register machines. Theoretical Computer Science 168(2), 267–301 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Neary, T.: Presentation at Computing with Biomolecules (CBM (2008), http://www.emcc.at/UC2008/Presentations/CBM5.pdf
  4. 4.
    Neary, T.: On the computational complexity of spiking neural P systems. In: Calude, C.S., Costa, J.F., Freund, R., Oswald, M., Rozenberg, G. (eds.) UC 2008. LNCS, vol. 5204, pp. 189–205. Springer, Heidelberg (2008)Google Scholar
  5. 5.
    Neary, T.: A small universal spiking neural P system. In: Csuhaj-Varjú, E., Freund, R., Oswald, M., Salomma, K. (eds.) International Workshop on Computing with Biomolecules, Vienna, August 2008, pp. 65–74. Austrian Computer Society (2008)Google Scholar
  6. 6.
    Neary, T.: A boundary between universality and non-universality in spiking neural P systems (December 2009), arXiv:0912.0741v1 [cs.CC]Google Scholar
  7. 7.
    Pan, L., Zeng, X.: A note on small universal spiking neural P systems. In: Păun, G., Pérez-Jiménez, M.J., Riscos-Núñez, A. (eds.) Tenth Workshop on Membrane Computing (WMC10), Curtea de Argeş, Romania, August 2009, pp. 464–475 (2009)Google Scholar
  8. 8.
    Păun, A., Păun, G.: Small universal spiking neural P systems. BioSystems 90(1), 48–60 (2007)CrossRefGoogle Scholar
  9. 9.
    Păun, G., Pérez-Jiménez, M.J.: Spiking Neural P Systems. Recent Results, Research Topics. In: Algorithmic Bioprocesses. Natural Computing Series, pp. 273–291. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  10. 10.
    Zhang, X., Zeng, X., Pan, L.: Smaller universal spiking neural P systems. Fundamenta Informaticae 87(1), 117–136 (2008)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Turlough Neary
    • 1
  1. 1.Boole Centre for Research in InformaticsUniversity College CorkIreland

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