Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds of Algebraic Branching Programs and Layerization   In this paper we improve the lower bound of Chatterjee et al.\ (ECCC 2019) to
an $\Omega(n^2)$ lower bound for unlayered Algebraic Branching Programs. We
also
  study the impact layerization has on Algebraic Branching Programs. We exhibit
a polynomial that has an unlayered ABP of size $O(n)$ but any layered ABP has
size at least $\Omega(n\sqrt{n})$.
  We exhibit a similar dichotomy in the non-commutative setting where the
unlayered ABP has size $O(n)$ and any layered ABP has size at least
$\Omega(n\log n -\log^2 n)$.

2
The categories of this paper are: math
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an