Noise threshold for universality of 2-input gates

Evans and Pippenger showed in 1998 that e-noisy gates with 2 inputs are universal for arbitrary computation (i.e. can compute any function with bounded error), if all gates fail independently with probability isin and isin< isin₀ = (3 - radic7)/4 ap8.856%. We show that formulas built from gates with 2 inputs, in which each gate fails with probability at least isin₀ cannot be universal. Hence, there is a threshold on the tolerable noise for formulas with 2-input gates and it is isin₀. We conjecture that the same threshold also holds for circuits.