Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic Solutions of Equations in the Braid Group   Given a system of equations in a "random" finitely generated subgroup of the
braid group, we show how to find a small ordered list of elements in the
subgroup, which contains a solution to the equations with a significant
probability. Moreover, with a significant probability, the solution will be the
first in the list. This gives a probabilistic solution to: The conjugacy
problem, the group membership problem, the shortest representation of an
element, and other combinatorial group-theoretic problems in random subgroups
of the braid group.
  We use a memory-based extension of the standard length-based approach, which
in principle can be applied to any group admitting an efficient, reasonably
behaving length function.

15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin