#### 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

#### Published In

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