Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: When are dual Cayley automaton semigroups finite?   In this note we prove that, for a finite semigroup $S$, the dual
  Cayley automaton semigroup $\mathbf{C^{\ast}}(S)$ is finite if and only if
$S$ is $\mathcal{H}$-trivial and has no non-trivial right zero subsemigroups.

8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin