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Using Nondeterminism to Amplify Hardness

2006
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SIAM journal on computing (Print)
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We revisit the problem of hardness amplification in N P, as recently studied by O'Donnell (STOC '02). We prove that if N P has a balanced function f such that any circuit of size s(n) fails to compute f on a 1/ poly(n) fraction of inputs, then N P has a function f such that any circuit of size s (n) = s( √ n) Ω(1) fails to compute f on a 1/2 − 1/s (n) fraction of inputs. In particular, 1. If s(n) = n ω(1) , we amplify to hardness 1/2 − 1/n ω(1) . 2. If s(n) = 2 n Ω(1) , we amplify to hardness

doi:10.1137/s0097539705447281
fatcat:ulfaf5cazzeppah3svqctlb3im