Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Complexity of Factors of Multivariate Polynomials   The existence of string functions, which are not polynomial time computable,
but whose graph is checkable in polynomial time, is a basic assumption in
cryptography. We prove that in the framework of algebraic complexity, there are
no such families of polynomial functions of polynomially bounded degree over
fields of characteristic zero. The proof relies on a polynomial upper bound on
the approximative complexity of a factor g of a polynomial f in terms of the
(approximative) complexity of f and the degree of the factor g. This extends a
result by Kaltofen (STOC 1986). The concept of approximative complexity allows
to cope with the case that a factor has an exponential multiplicity, by using a
perturbation argument. Our result extends to randomized (two-sided error)
decision complexity.

16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
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
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin