Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: NE is not NP Turing Reducible to Nonexpoentially Dense NP Sets   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 $NE\not\subseteq NP_(NP \cap$
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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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex