On reliable computation by noisy random Boolean formulas

Abstract

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 gates. We show that these gates can be used to compute any Boolean function reliably below the noise bound.

arXiv commentA new version with improved presentation accepted for publication in IEEE TRANSACTIONS ON INFORMATION THEORY