On the maximum tolerable noise for reliable computation by formulas

It is shown that if formulas constructed from error-prone three-input gates are used to compute Boolean functions, then a per-gate failure probability of 1/6 or more cannot be tolerated. The result is shown to be tight if the per-gate failure probability is constant and precisely known.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>