Hardness Amplification within NP against Deterministic Algorithms

Abstract

We study the average-case hardness of the class NP against deterministic polynomial time algorithms. We prove that there exists some constant mu Gt 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)-mu 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)-mu 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.