Improved hardness amplification in NP
We study the problem of hardness amplification in NP. We prove that if there is a balanced
function in NP such that any circuit of size s (n)= 2Ω (n) fails to compute it on a 1/poly (n)
fraction of inputs, then there is a function in NP such that any circuit of size s′(n) fails to
compute it on a 1/2− 1/s′(n) fraction of inputs, with [Formula: see text]. This improves the
result of Healy et al.(STOC'04), which only achieves [Formula: see text] for the case with s
(n)= 2Ω (n).
function in NP such that any circuit of size s (n)= 2Ω (n) fails to compute it on a 1/poly (n)
fraction of inputs, then there is a function in NP such that any circuit of size s′(n) fails to
compute it on a 1/2− 1/s′(n) fraction of inputs, with [Formula: see text]. This improves the
result of Healy et al.(STOC'04), which only achieves [Formula: see text] for the case with s
(n)= 2Ω (n).
We study the problem of hardness amplification in NP. We prove that if there is a balanced function in NP such that any circuit of size s(n)=2Ω(n) fails to compute it on a 1/poly(n) fraction of inputs, then there is a function in NP such that any circuit of size s′(n) fails to compute it on a 1/2−1/s′(n) fraction of inputs, with [Formula: see text] . This improves the result of Healy et al. (STOC’04), which only achieves [Formula: see text] for the case with s(n)=2Ω(n).
Elsevier