Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weakening Assumptions for Deterministic Subexponential Time Non-Singular
  Matrix Completion   In (Kabanets, Impagliazzo, 2004) it is shown how to decide the circuit
polynomial identity testing problem (CPIT) in deterministic subexponential
time, assuming hardness of some explicit multilinear polynomial family for
arithmetical circuits. In this paper, a special case of CPIT is considered,
namely low-degree non-singular matrix completion (NSMC). For this subclass of
problems it is shown how to obtain the same deterministic time bound, using a
weaker assumption in terms of determinantal complexity.
  Hardness-randomness tradeoffs will also be shown in the converse direction,
in an effort to make progress on Valiant's VP versus VNP problem. To separate
VP and VNP, it is known to be sufficient to prove that the determinantal
complexity of the m-by-m permanent is $m^{\omega(\log m)}$. In this paper it is
shown, for an appropriate notion of explicitness, that the existence of an
explicit multilinear polynomial family with determinantal complexity
m^{\omega(\log m)}$ is equivalent to the existence of an efficiently computable
generator $G_n$ for multilinear NSMC with seed length $O(n^{1/\sqrt{\log n}})$.
The latter is a combinatorial object that provides an efficient deterministic
black-box algorithm for NSMC. ``Multilinear NSMC'' indicates that $G_n$ only
has to work for matrices $M(x)$ of $poly(n)$ size in $n$ variables, for which
$det(M(x))$ is a multilinear polynomial.

15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int