Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partial Boolean functions with exact quantum 1-query complexity   We provide two sufficient and necessary conditions to characterize any
$n$-bit partial Boolean function with exact quantum 1-query complexity. Using
the first characterization, we present all $n$-bit partial Boolean functions
that depend on $n$ bits and have exact quantum 1-query complexity. Due to the
second characterization, we construct a function $F$ that maps any $n$-bit
partial Boolean function to some integer, and if an $n$-bit partial Boolean
function $f$ depends on $k$ bits and has exact quantum 1-query complexity, then
$F(f)$ is non-positive. In addition, we show that the number of all $n$-bit
partial Boolean functions that depend on $k$ bits and have exact quantum
1-query complexity is not bigger than $n^{2}2^{2^{n-1}(1+2^{2-k})+2n^{2}}$ for
all $n\geq 3$ and $k\geq 2$.

24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an