Matrix Representation of Spiking Neural P Systems

  • Xiangxiang Zeng
  • Henry Adorna
  • Miguel Ángel Martínez-del-Amor
  • Linqiang Pan
  • Mario J. Pérez-Jiménez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6501)

Abstract

Spiking neural P systems (SN P systems, for short) are a class of distributed parallel computing devices inspired from the way neurons communicate by means of spikes. In this work, a discrete structure representation of SN P systems with extended rules and without delay is proposed. Specifically, matrices are used to represent SN P systems. In order to represent the computations of SN P systems by matrices, configuration vectors are defined to monitor the number of spikes in each neuron at any given configuration; transition net gain vectors are also introduced to quantify the total amount of spikes consumed and produced after the chosen rules are applied. Nondeterminism of the systems is assured by a set of spiking transition vectors that could be used at any given time during the computation. With such matrix representation, it is quite convenient to determine the next configuration from a given configuration, since it involves only multiplication and addition of matrices after deciding the spiking transition vector.

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References

  1. 1.
    Cavaliere, M., Egecioglu, O., Ibarra, O.H., Woodworth, S., Ionescu, M., Păun, G.: Asynchronous Spiking Neural P Systems. Theoretical Computer Science 410, 2352–2364 (2009)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Gutiérrez-Naranjo, M.A., Pérez-Jiménez, M.J.: Searching Previous Configurations in Membrane Computing. In: Păun, G., Pérez-Jiménez, M.J., Riscos-Núñez, A., Rozenberg, G., Salomaa, A. (eds.) WMC 2009. LNCS, vol. 5957, pp. 301–315. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Ionescu, M., Păun, G., Yokomori, T.: Spiking Neural P Systems. Fundamenta Informaticae 71(2–3), 279–308 (2006)MathSciNetMATHGoogle Scholar
  4. 4.
    Ionescu, M., Păun, G., Yokomori, T.: Spiking Neural P Systems with Exhaustive Use of Rules. International Journal of Unconventional Computing 3, 135–154 (2007)Google Scholar
  5. 5.
    Nelson, J.K., McCormac, J.C.: Structural Analysis: Using Classical and Matrix Methods, 3rd edn. Wiley, Chichester (2003)Google Scholar
  6. 6.
    Păun, G.: Computing with Membranes. Journal of Computer and System Sciences 61(1), 108–143 (2000)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Păun, G.: Membrane Computing – An Introduction. Springer, Berlin (2002)CrossRefMATHGoogle Scholar
  8. 8.
    Păun, G., Rozenberg, G., Salomaa, A. (eds.): Handbook of Membrane Computing. Oxford University Press, Oxford (2010)MATHGoogle Scholar
  9. 9.
    Wang, J., Hoogeboom, H.J., Pan, L., Păun, G., Pérez-Jiménez, M.J.: Spiking Neural P Systems with Weights. Neural Computation 22(10), 2615–2646 (2010)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    The P System Web Page, http://ppage.psystems.eu

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Xiangxiang Zeng
    • 1
  • Henry Adorna
    • 2
  • Miguel Ángel Martínez-del-Amor
    • 3
  • Linqiang Pan
    • 1
  • Mario J. Pérez-Jiménez
    • 3
  1. 1.Image Processing and Intelligent Control Key Laboratory of Education Ministry, Department of Control Science and EngineeringHuazhong University of Science and TechnologyWuhanChina
  2. 2.Department of Computer Science, (Algorithms and Complexity)University of the PhilippinesQuezon CityPhilippines
  3. 3.Research Group on Natural Computing, Department of Computer Science and Artificial IntelligenceUniversity of SevillaSevillaSpain

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