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### Paper:

TR10-196 | 8th December 2010 23:05

#### NE is not NP Turing Reducible to Nonexpoentially Dense NP Sets

TR10-196
Authors: Bin Fu
Publication: 13th December 2010 23:34
Downloads: 3027
Keywords:

Abstract:

A long standing open problem in the computational complexity theory
is to separate NE from BPP, which is a subclass of $NP_T (NP\cap P/poly)$.
In this paper, we show that $NE\not\subseteq NP_T (NP \cap$ Nonexponentially-Dense-Class),
where Nonexponentially-Dense-Class is the class of languages A without exponential density
(for each constant c>0,$|A^{\le n}|\le 2^{n^c}$ for infinitely many integers n).

Our result implies $NE\not\subseteq NP_T({pad(NP, g(n))})$ for every time
constructible super-polynomial function g(n) such as
$g(n)=n^{\ceiling{\log\ceiling{\log n}}}$, where Pad(NP, g(n))
is class of all languages $L_B=\{s10^{g(|s|)-|s|-1}:s\in B\}$ for
$B\in NP$. We also show $NE\not\subseteq NP_T(P_{tt}(NP)\cap Tally)$.

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