Deterministic Hardness Amplification via Local GMD Decoding.
Parikshit Gopalan, Venkatesan Guruswami · Electronic colloquium on computational complexity · 2007
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) 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) 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.