Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorizations of the Thompson-Higman groups, and circuit complexity   We consider the subgroup lpG_{k,1} of length preserving elements of the
Thompson-Higman group G_{k,1} and we show that all elements of G_{k,1} have a
unique lpG_{k,1}.F_{k,1} factorization. This applies to the Thompson-Higman
group T_{k,1} as well. We show that lpG_{k,1} is a ``diagonal'' direct limit of
finite symmetric groups, and that lpT_{k,1} is a k^infinity Pr"ufer group. We
find an infinite generating set of lpG_{k,1} which is related to reversible
boolean circuits.
  We further investigate connections between the Thompson-Higman groups,
circuits, and complexity. We show that elements of F_{k,1} cannot be one-way
functions. We show that describing an element of G_{k,1} by a generalized
bijective circuit is equivalent to describing the element by a word over a
certain infinite generating set of G_{k,1}; word length over these generators
is equivalent to generalized bijective circuit size.
  We give some coNP-completeness results for G_{k,1} (e.g., the word problem
when elements are given by circuits), and #P-completeness results (e.g.,
finding the lpG_{k,1}.F_{k,1} factorization of an element of G_{k,1} given by a
circuit).

3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom