Complexity of Boolean Computations for a Spiking Neuron

We investigate the computational power of a model for 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 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.