Abstract
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.
Turlough Neary is funded by Science Foundation Ireland Research Frontiers Programme grant number 07/RFP/CSMF641. I would also like to thank Damien Woods for his helpful suggestions and comments.
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Neary, T. (2010). A Boundary between Universality and Non-universality in Extended Spiking Neural P Systems. In: Dediu, AH., Fernau, H., MartÃn-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2010. Lecture Notes in Computer Science, vol 6031. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13089-2_40
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DOI: https://doi.org/10.1007/978-3-642-13089-2_40
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