Hardness amplification within NP

We study the average-case hardness of the class NP against deterministic polynomial time algorithms. We prove that there exists some constant ? > 0 such that if there is some language in NP for which no deterministic polynomial time algorithm can decide L correctly on a 1 - (log n)-? fraction of inputs of length n, then there is a language L in NP for which no deterministic polynomial time algorithm can decide L correctly on a 3/4 + (log n)-? fraction of inputs of length n. In coding theoretic terms, we give a construction of a monotone code that can be uniquely decoded up to error rate 1 4 by a deterministic local decoder.

• Type: Conference
• Year: 2002
• Where: STOC
• Authors: Ryan O'Donnell
• Keywords: Algorithms, Deterministic Local Decoder, Deterministic Polynomial Time, Polynomial Time Algorithm, STOC 2002