Abstract
We prove that the size of any read-once de Morgan formula reduces on average by a factor of at least p α − o(1) when all but a fraction p of the input variables are randomly assigned to {0,1} (here α α l log 2(√5 − 1) ≈ 3.27 ). This resolves in the affirmative a conjecture of Paterson and Zwick. The bound is shown to be tight up to a polylogarithmic factor for all p ⩾ n − 1 α .
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