On the Eeect of Analog Noise in Discrete-time Analog Computations

We introduce a model for noise-robust analog computations with discrete time that is exible enough to cover the most important concrete cases, such as computations in noisy analog neural nets and networks of noisy spiking neurons. We show that the presence of arbitrarily small amounts of analog noise reduces the power of analog computational models to that of nite automata, and we also prove a new type of upper bound for the VC-dimension of computational models with analog noise.