Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Graph Induced Symbolic Systems   \begin{abstract} In this paper, we investigate a shift arising from graph
$G$. We prove that any $k$-dimensional shift of finite type can be generated
through a $k$-dimensional graph. We investigate the structure of the shift
space using the generating matrices for the shift space. We prove that a two
dimensional shift space has a horizontally (vertically) periodic point if and
only if it possesses a $(m,n)$-periodic point (for some $m,n\in
\mathbb{Z}\setminus \{0\}$). We prove that a shift space is finite if and only
if it can be generated by permutation matrices. We study the non-emptiness
problem and existence of periodic points in terms of the generating matrices.

37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph