Abstract
A k-output spiking neural P system (SNP) with output neurons, O 1, ..., O k , generates a tuple (n 1, ..., n k ) of positive integers if, starting from the initial configuration, there is a sequence of steps such that during the computation, each O i generates exactly two spikes a a (the times the pair a a are generated may be different for different output neurons) and the time interval between the first a and the second a is n i . After the output neurons generate their pairs of spikes, the system eventually halts. We give characterizations of sets definable by partially blind multicounter machines in terms of k-output SNPs operating in a sequential mode. Slight variations of the models make them universal.
The research of O. H. Ibarra and S. Woodworth was supported in part by NSF Grants CCF-0430945 and CCF-0524136. The research of A. Păun was supported in part by NSF Grant CCF-0523572.
This is a preview of subscription content, log in via an institution to check access.
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, Cambridge (2002)
Greibach, S.: Remarks on blind and partially blind one-way multicounter machines. Theoretical Computer Science 7(3), 311–324 (1978)
Ibarra, O., Păun, A., Păun, G., Rodriguez-Paton, A., Sosik, P., Woodworth, S.: Normal forms for spiking neural P systems. In: Proc. Fourth Brainstorming Week on Membrane Computing, Fenix Editora, Sevilla, vol. II (2006), (also available at [11])
Ionescu, M., Păun, Gh., Yokomori, T.: Spiking neural P systems. Fundamenta Informaticae 71(2-3), 279–308 (2006)
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)
Păun, Gh.: Membrane Computing – An Introduction. Springer, Berlin (2002)
Păun, Gh., Pérez-Jiménez, M.J., Rozenberg, G.: Spike trains in spiking neural P systems. Intern. J. Found. Computer Sci. (to appear, also available at [11])
Păun, Gh., Pérez-Jiménez, M.J., Rozenberg, G.: Infinite spike trains in spiking neural P systems (submitted, 2006)
The P Systems Web Page, http://psystems.disco.unimib.it
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ibarra, O.H., Woodworth, S., Yu, F., Păun, A. (2006). On Spiking Neural P Systems and Partially Blind Counter Machines. In: Calude, C.S., Dinneen, M.J., Păun, G., Rozenberg, G., Stepney, S. (eds) Unconventional Computation. UC 2006. Lecture Notes in Computer Science, vol 4135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11839132_10
Download citation
DOI: https://doi.org/10.1007/11839132_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38593-6
Online ISBN: 978-3-540-38594-3
eBook Packages: Computer ScienceComputer Science (R0)