Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite state automata and homeomorphism of self-similar sets   The topological and metrical equivalence of fractals is an important topic in
analysis. In this paper, we use a class of finite state automata, called
$\Sigma$-automaton, to construct psuedo-metric spaces, and then apply them to
the study of classification of self-similar sets. We first introduce a notion
of topology automaton of a fractal gasket, which is a simplified version of
neighbor automaton; we show that a fractal gasket is homeomorphic to the
psuedo-metric space induced by the topology automaton. Then we construct a
universal map to show that psuedo-metric spaces induced by different automata
can be bi-Lipschitz equivalent. As an application, we obtain a rather general
sufficient condition for two fractal gaskets to be homeomorphic or Lipschitz
equivalent.

17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con