On Reliable Computation by Noisy Random Boolean Formulas
Alexander Mozeika, David Saad · IEEE Transactions on Information Theory · 2014
We study noisy computation in randomly generated k-ary Boolean formulas. We establish bounds on the noise level above which the results of computation by random formulas are not reliable. This bound is saturated by formulas constructed from a single majority-like gate. We show that these gates can be used to compute any Boolean function reliably below the noise bound.