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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Gerstner, W., Kistler, W.: Spiking Neuron Models. Single Neurons, Populations, Plasticity. Cambridge Univ. Press (2002)
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
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)
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)
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)
Ionescu, M., Păun, G., Yokomori, T.: Spiking neural P systems. Fundamenta Informaticae 71(2-3), 279–308 (2006)
Korec, I.: Small universal register machines. Theoretical Computer Science 168, 267–301 (1996)
Maass, W.: Computing with spikes. Special Issue on Foundations of Information Processing of TELEMATIK 8(1), 32–36 (2002)
Maass, W., Bishop, C. (eds.): Pulsed Neural Networks. MIT Press, Cambridge (1999)
Minsky, M.: Computation – Finite and Infinite Machines. Prentice Hall, Englewood Cliffs (1967)
Naksinehaboon, N., et al.: High Performance Computing Systems with Various Checkpointing Schemes. International Journal of Computers Communications & Control 4(4), 386–400 (2009)
Păun, A., Păun, G.: Small universal spiking neural P systems. BioSystems 90(1), 48–60 (2007)
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
Păun, G.: Membrane Computing – An Introduction. Springer, Berlin (2002)
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)
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)
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)
Neary, T.: On the computational complexity of spiking neural P systems. Natural Computing 9(4), 831–851 (2010)
Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages, 3rd edn. Springer, Berlin (1997)
Scott, S.L., et al.: A Tunable Holistic Resiliency Approach for High-Performance Computing Systems. ACM Sigplan Notices 44(4), 305–306 (2009)
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)
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)
Zhang, X., Zeng, X., Pan, L.: Smaller universal spiking neural P systems. Fundamenta Informaticae 87(1), 117–136 (2008)
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)
The P Systems Web Page, http://ppage.psystems.eu
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)