Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Randomized and Quantum Query Complexities   We study randomized and quantum query (a.k.a. decision tree) complexity for
all total Boolean functions, with emphasis to derandomization and
dequantization (removing quantumness from algorithms). Firstly, we show that
$D(f) = O(Q_1(f)^3)$ for any total function $f$, where $D(f)$ is the minimal
number of queries made by a deterministic query algorithm and $Q_1(f)$ is the
number of queries made by any quantum query algorithm (decision tree analog in
quantum case) with one-sided constant error; both algorithms compute function
$f$. Secondly, we show that for all total Boolean functions $f$ holds
$R_0(f)=O(R_2(f)^2 \log N)$, where $R_0(f)$ and $R_2(f)$ are randomized
zero-sided (a.k.a Las Vegas) and two-sided (a.k.a. Monte Carlo) error query
complexities.

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The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
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The categories of this paper are: math
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The categories of this paper are: funct-an