Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The pseudo-Anosov and conjugacy problems are in $\textbf{NP} \cap
  \textbf{co-NP}$   For a fixed marked surface $S$, we construct polynomial bounds on the
periodic and preperiodic lengths of the maximal splitting sequences of a
projectively invariant measured train track.
  We give two consequences of these bounds. Firstly, that the problem of
deciding whether a mapping class is pseudo-Anosov lies in $\textbf{NP}$. This
is dual to the previously known result that the pseudo-Anosov problem is in
$\textbf{co-NP}$. Secondly, that the problem of deciding whether two mapping
classes are conjugate lies in $\textbf{co-NP}$. Similarly, this is the dual to
the previously known result that the conjugacy problem is in $\textbf{NP}$.
  As usual, in both cases we immediately obtain exponential time solutions to
these problems. A version of these algorithms have been implemented as part of
flipper.

25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ