Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Search and witness problems in group theory   Decision problems are problems of the following nature: given a property P
and an object O, find out whether or not the object O has the property P. On
the other hand, witness problems are: given a property P and an object O with
the property P, find a proof of the fact that O indeed has the property P. On
the third hand(?!), search problems are of the following nature: given a
property P and an object O with the property P, find something "material"
establishing the property P; for example, given two conjugate elements of a
group, find a conjugator. In this survey our focus is on various search
problems in group theory, including the word search problem, the subgroup
membership search problem, the conjugacy search problem, and others.

10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph