Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A polynomial-time solution to the reducibility problem   We propose an algorithm for deciding whether a given braid is pseudo-Anosov,
reducible, or periodic. The algorithm is based on Garside's weighted
decomposition and is polynomial-time in the word-length of an input braid.
Moreover, a reduction system of circles can be found completely if the input is
a certain type of reducible braids.

13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics