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.