On the Effect of Analog Noise in Discrete-Time Analog Computation

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