Date of Original Version

5-2003

Type

Article

Abstract or Description

It is known that for all monotone functions f : {0, 1}n → {0, 1}, if x ∈ {0, 1}n is chosen uniformly at random and y is obtained from x by flipping each of the bits of x independently with probability ϵ = n−α, then P[f(x) ≠ f(y)] < cn−α+1/2, for some c > 0. We also study the problem of achieving the best dependence on δ in the case that the noise rate ϵ is at least a small constant; the results we obtain are tight to within logarithmic factors.

DOI

10.1002/rsa.10097

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Published In

Random Structures & Algorithms , 23, 3, 333-350.