Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measuring cones and other thick subsets in free groups   In this paper we investigate the special automata over finite rank free
groups and estimate asymptotic characteristics of sets they accept. We show how
one can decompose an arbitrary regular subset of a finite rank free group into
disjoint union of sets accepted by special automata or special monoids. These
automata allow us to compute explicitly generating functions,
$\lambda-$measures and Cesaro measure of thick monoids. Also we improve the
asymptotic classification of regular subsets in free groups.

8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn