Using nondeterminism to amplify hardness

We revisit the problem of hardness amplification in NP, as recently studied by O'Donnell (STOC `02). We prove that if NP 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 NP has a function f such that any circuit of size s (n) = s( n)(1) fails to compute f on a 1/2-1/s (n) fraction of inputs. In particular,

• Type: Conference
• Year: 2004
• Where: STOC
• Authors: Alexander Healy, Salil P. Vadhan, Emanuele Viola
• Keywords: Algorithms, Hardness Amplification, STOC 2004