Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automatic structures and boundaries for graphs of groups   We study the synchronous and asynchronous automatic structures on the
fundamental group of a graph of groups in which each edge group is finite. Up
to a natural equivalence relation, the set of biautomatic structures on such a
graph product bijects to the product of the sets of biautomatic structures on
the vertex groups. The set of automatic structures is much richer. Indeed, it
is dense in the infinite product of the sets of automatic structures of all
conjugates of the vertex groups. We classify these structures by a class of
labelled graphs which ``mimic" the underlying graph of the graph of groups.
Analogous statements hold for asynchronous automatic structures. We also
discuss the boundaries of these structures.

11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph