Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower bound for monotone Boolean convolution   Any monotone Boolean circuit computing the $n$-dimensional Boolean
convolution requires at least $n^2$ and-gates. This precisely matches the
obvious upper bound.

33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin