On networks of noisy gates

We show that many Boolean functions (including, in a certain sense, "almost all" Boolean functions) have the property that the number of noisy gates needed to compute them differs from the number of noiseless gates by at most a constant factor. This may be contrasted with results of von Neumann, Dobrushin and Ortyukov to the effect that (1) for every Boolean function, the number of noisy gates needed is larger by at most a logarithmic factor, and (2) for some Boolean functions, it is larger by at least a logarithmic factor.