Skip to main content
SpringerLink
Log in

Sequentiality Induced by Spike Number in SNP Systems: Small Universal Machines

  • Conference paper
Membrane Computing (CMC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7184))

Included in the following conference series:

Abstract

In this paper we consider sequential SNP systems where the sequentiality of the system is induced by the max-spike: the neuron with the maximum number of spikes out of the neurons that can spike at one step will fire. This corresponds to a global view of the whole network that makes the system sequential. We continue the study in the direction of max-spike and show that systems with 132 neurons are universal. This improves a recent result in the area.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gerstner, W., Kistler, W.: Spiking Neuron Models. Single Neurons, Populations, Plasticity. Cambridge Univ. Press (2002)

    Google Scholar 

  2. Gottumukkala, N.R., et al.: Reliability of a System of k Nodes for High Performance Computing Applications. IEEE Transactions on Reliability 59(1), 162–169 (2010), doi:10.1109/TR.2009.2034291

    Article  Google Scholar 

  3. Ibarra, O.H., Păun, A., Rodriguez-Paton, A.: Sequential SNP systems based on min/max spike number. Theoretical Computer Science 410(30-32), 2982–2991 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ibarra, O.H., Păun, A., Rodríguez-Patón, A.: Sequentiality Induced by Spike Number in SNP Systems. In: Goel, A., Simmel, F.C., Sosík, P. (eds.) DNA 14. LNCS, vol. 5347, pp. 179–190. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  5. Ibarra, O.H., Woodworth, S., Yu, F., Păun, A.: On Spiking Neural P Systems and Partially Blind Counter Machines. In: Calude, C.S., Dinneen, M.J., Păun, G., Rozenberg, G., Stepney, S. (eds.) UC 2006. LNCS, vol. 4135, pp. 113–129. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Ionescu, M., Păun, G., Yokomori, T.: Spiking neural P systems. Fundamenta Informaticae 71(2-3), 279–308 (2006)

    MathSciNet  MATH  Google Scholar 

  7. Korec, I.: Small universal register machines. Theoretical Computer Science 168, 267–301 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Maass, W.: Computing with spikes. Special Issue on Foundations of Information Processing of TELEMATIK 8(1), 32–36 (2002)

    Google Scholar 

  9. Maass, W., Bishop, C. (eds.): Pulsed Neural Networks. MIT Press, Cambridge (1999)

    MATH  Google Scholar 

  10. Minsky, M.: Computation – Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)

    MATH  Google Scholar 

  11. Naksinehaboon, N., et al.: High Performance Computing Systems with Various Checkpointing Schemes. International Journal of Computers Communications & Control 4(4), 386–400 (2009)

    Article  Google Scholar 

  12. Păun, A., Păun, G.: Small universal spiking neural P systems. BioSystems 90(1), 48–60 (2007)

    Article  MATH  Google Scholar 

  13. Paun, A., Paun, M., Rodriguez-Paton, A.: On the Hopcroft’s minimization technique for DFA and DFCA. Theoretical Computer Science 410(24-25), 2424–2430 (2009), doi:10.1016/j.tcs.2009.02.034

    Article  MathSciNet  MATH  Google Scholar 

  14. Păun, G.: Membrane Computing – An Introduction. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  15. Păun, G., Pérez-Jiménez, M.J., Rozenberg, G.: Spike trains in spiking neural P systems. International Journal of Foundations of Computer Science 17(4), 975–1002 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Păun, G., Pérez-Jiménez, M.J., Rozenberg, G.: Spike trains in spiking neural P systems. International Journal of Foundations of Computer Science 17(4), 975–1002 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  17. Paun, M., Naksinehaboon, N., Nassar, R., Leangsuksun, C., Scott, S.L., Taerat, N.: Incremental Checkpoint Schemes For Weibull Failure Distribution. International Journal of Foundations of Computer Science 21(3), 329–344 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Neary, T.: On the computational complexity of spiking neural P systems. Natural Computing 9(4), 831–851 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, 3rd edn. Springer, Berlin (1997)

    MATH  Google Scholar 

  20. Scott, S.L., et al.: A Tunable Holistic Resiliency Approach for High-Performance Computing Systems. ACM Sigplan Notices 44(4), 305–306 (2009)

    Article  Google Scholar 

  21. Strimbu, B.M., Innes, J.L., Strimbu, V.F.: A deterministic harvest scheduler using perfect bin-packing theorem. European Journal of Forest Research 129(5), 961–974 (2010)

    Article  Google Scholar 

  22. Strimbu, B.M., Hickey, G.M., Strimbu, V.G., Innes, J.L.: On the use of statistical tests with non-normaly distributed data in landscape change detection. Forest Science 55(1), 72–83 (2009)

    Google Scholar 

  23. Zhang, X., Zeng, X., Pan, L.: Smaller universal spiking neural P systems. Fundamenta Informaticae 87(1), 117–136 (2008)

    MathSciNet  MATH  Google Scholar 

  24. Zhang, X., Jiang, Y., Pan, L.: Small Universal Spiking Neural P Systems with Exhaustive Use of Rule. Journal of Computational and Theoretical Nanoscience 7(5), 890–899 (2010)

    Article  Google Scholar 

  25. The P Systems Web Page, http://ppage.psystems.eu

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Louisiana Tech University, Ruston, PO Box 10348, Louisiana, LA-71272, USA

    Andrei Păun

  2. Bioinformatics Department, National Institute of Research and Development for Biological Sciences, Splaiul Independenţei, Nr. 296, Sector 6, Bucharest, Romania

    Andrei Păun & Manuela Sidoroff

Authors
  1. Andrei Păun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manuela Sidoroff
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Computer Science, University of Sheffield, Regent Court, Portobello Street, S1 4DP, Sheffield, UK

    Marian Gheorghe

  2. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Gheorghe Păun

  3. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

  4. Turku Centre for Computer Science (TUCS), Leminkaisenkatu 14, 20520, Turku, Finland

    Arto Salomaa

  5. Faculté des Sciences et Technologie, Laboratoire d’Algorithmique, Complexité et Logique (LACL), Université Paris Est – Créteil Val de Marne, 61, av. Général de Gaulle, 94010, Créteil, France

    Sergey Verlan

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Păun, A., Sidoroff, M. (2012). Sequentiality Induced by Spike Number in SNP Systems: Small Universal Machines. In: Gheorghe, M., Păun, G., Rozenberg, G., Salomaa, A., Verlan, S. (eds) Membrane Computing. CMC 2011. Lecture Notes in Computer Science, vol 7184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28024-5_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-28024-5_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28023-8

  • Online ISBN: 978-3-642-28024-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation