Hardness amplification proofs require majority
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Hardness Amplification Proofs Require Majority
SIAM Journal on Computing
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We study the average-case hardness of the class NP against deterministic polynomial time algorithms. 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 − (log n)−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 + (log n)−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 1/4 by a deterministic local decoder.