Hardness amplification within NP against deterministic algorithms

摘要

We study the average-case hardness of the class NP against algorithms in P. We prove that there exists some constant μ>0 such that if there is some language in NP for which no deterministic polynomial time algorithm can decide L correctly on a 1−(logn)−μ 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+(logn)−μ 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 14 by a deterministic local decoder.