On reliable computation by noisy random Boolean formulas

TL;DR

This paper investigates the limits of reliable computation in noisy random Boolean formulas, identifying noise thresholds and demonstrating the use of majority-like gates for reliable computation below these thresholds.

Contribution

It establishes bounds on noise levels for reliable computation in random formulas and introduces majority-like gates as a means to achieve reliable Boolean function computation below these bounds.

Findings

Noise thresholds for reliable computation are identified.

Majority-like gates enable reliable computation below the noise bound.

Random formulas' computational reliability is limited by the noise level.

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.