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On computing Boolean functions by a spiking neuron

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Abstract

Computations by spiking neurons are performed using the timing of action potentials. We investigate the computational power of a simple model for such a spiking neuron in the Boolean domain by comparing it with traditional neuron models such as threshold gates (or McCulloch–Pitts neurons) and sigma-pi units (or polynomial threshold gates). In particular, we estimate the number of gates required to simulate a spiking neuron by a disjunction of threshold gates and we establish tight bounds for this threshold number. Furthermore, we analyze the degree of the polynomials that a sigma-pi unit must use for the simulation of a spiking neuron. We show that this degree cannot be bounded by any fixed value. Our results give evidence that the use of continuous time as a computational resource endows single-cell models with substantially larger computational capabilities.

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  1. Lehrstuhl Mathematik und Informatik, Fakultät für Mathematik, Ruhr-, Universität Bochum, D-44780, Bochum, Germany

    Michael Schmitt

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  1. Michael Schmitt
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Schmitt, M. On computing Boolean functions by a spiking neuron. Annals of Mathematics and Artificial Intelligence 24, 181–191 (1998). https://doi.org/10.1023/A:1018953300185

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