Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extended finite automata and decision problems for matrix semigroups   We make a connection between the subgroup membership and identity problems
for matrix groups and extended finite automata. We provide an alternative proof
for the decidability of the subgroup membership problem for $ 2 \times 2 $
integer matrices. We show that the emptiness problem for extended finite
automata over $ 4 \times 4 $ integer matrix semigroups is undecidable. We prove
that the decidability of the universe problem for extended finite automata is a
sufficient condition for the decidability of the subgroup membership and
identity problems.

13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int