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. © 2010 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Neary, T. (2010). A boundary between universality and non-universality in extended spiking neural P systems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6031 LNCS, pp. 475–487). https://doi.org/10.1007/978-3-642-13089-2_40
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