Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hardness of the Determinant: Sum of Regular Set-Multilinear
  Circuits   In this paper, we study the computational complexity of the commutative
determinant polynomial computed by a class of set-multilinear circuits which we
call regular set-multilinear circuits. Regular set-multilinear circuits are
commutative circuits with a restriction on the order in which they can compute
polynomials. A regular circuit can be seen as the commutative analogue of the
ordered circuit defined by Hrubes,Wigderson and Yehudayoff [HWY10]. We show
that if the commutative determinant polynomial has small representation in the
sum of constantly many regular set-multilinear circuits, then the commutative
permanent polynomial also has a small arithmetic circuit.

4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph