Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Asymptotically Tight Bound on the Number of Relevant Variables in a
  Bounded Degree Boolean Function   We prove that there is a constant $C\leq 6.614$ such that every Boolean
function of degree at most $d$ (as a polynomial over $\mathbb{R}$) is a $C\cdot
2^d$-junta, i.e. it depends on at most $C\cdot 2^d$ variables. This improves
the $d\cdot 2^{d-1}$ upper bound of Nisan and Szegedy [Computational Complexity
4 (1994)]. Our proof uses a new weighting scheme where we assign weights to
variables based on the highest degree monomial they appear on.
  The bound of $C\cdot 2^d$ is tight up to the constant $C$ as a lower bound of
$2^d-1$ is achieved by a read-once decision tree of depth $d$. We slightly
improve the lower bound by constructing, for each positive integer $d$, a
function of degree $d$ with $3\cdot 2^{d-1}-2$ relevant variables. A similar
construction was independently observed by Shinkar and Tal.

27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th