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Deterministic Hardness Amplification via Local GMD Decoding (2007)
| Venue: | ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 89 |
| Citations: | 1 - 1 self |
BibTeX
@MISC{Gopalan07deterministichardness,
author = {Parikshit Gopalan and Venkatesan Guruswami},
title = {Deterministic Hardness Amplification via Local GMD Decoding},
year = {2007}
}
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Abstract
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 by a deterministic local decoder. can be uniquely decoded up to error rate 1/4
