On uniform amplification of hardness in NP

We continue the study of amplification of average-case complexity within NP, and we focus on the uniform case. We prove that if every problem in NP admits an efficient uniform algorithm that (averaged over random inputs and over the internal coin tosses of the algorithm) succeeds with probability at least 1/2 + 1/(log n) , then for every problem in NP there is an efficient uniform algorithm that succeeds with probability at least 1 - 1/poly(n). Above, > 0 is an absolute constant. Previously, Trevisan (FOCS'03) presented a similar reduction between success 3/4 + 1/(log n) and 1 - 1/(log n) . Stronger reductions, due to O'Donnell (STOC'02) and Healy, Vadhan and Viola (FOCS'04) are known in the non-uniform case.

• Type: Conference
• Year: 2005
• Where: STOC
• Authors: Luca Trevisan
• Keywords: Algorithms, Efficient Uniform Algorithm, Internal Coin Tosses, STOC 2005, Uniform Case