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Hardness Amplification within NP against Deterministic Algorithms

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2 Author(s)
Gopalan, P. ; Univ. of Washington, Seattle, WA ; Guruswami, V.

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.

Published in:

Computational Complexity, 2008. CCC '08. 23rd Annual IEEE Conference on

Date of Conference:

23-26 June 2008