Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automatic semigroups vs automaton semigroups   We develop an effective and natural approach to interpret any semigroup
admitting a special language of greedy normal forms as an automaton
semigroup,namely the semigroup generated by a Mealy automaton encoding the
behaviour of such a language of greedy normal forms under one-sided
multiplication.The framework embraces many of the well-known classes of
(automatic) semigroups: finite monoids, free semigroups, free commutative
monoids, trace or divisibility monoids, braid or Artin-Tits or Krammer or
Garside monoids, Baumslag-Solitar semigroups, etc.Like plactic monoids or
Chinese monoids, some neither left- nor right-cancellative automatic semigroups
are also investigated, as well as some residually finite variations of the
bicyclic monoid. It provides what appears to be the first known connection from
a class of automatic semigroupsto a class of automaton semigroups. It is
worthwhile noting that, in all these cases, "being an automatic semigroup" and
"being an automaton semigroup" become dual properties in a very
automata-theoretical sense. Quadratic rewriting systems and associated tilings
appear as a cornerstone of our construction.

15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: stat
12
The categories of this paper are: nucl-th