Noise threshold for universality of 2-input gates
نویسنده
چکیده
Evans and Pippenger showed in 1998 that -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 and < 0 = (3 − √ 7)/4 ≈ 8.856%. We show that formulas built from gates with 2 inputs, in which each gate fails with probability at least 0 cannot be universal. Hence, there is a threshold on the tolerable noise for formulas with 2-input gates and it is 0. We conjecture that the same threshold also holds for circuits.
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