On Computing Boolean Functions by a Spiking Neuron

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 must be used
by sigma-pi units when simulating 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.