Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An analogue of Cobham's theorem for graph directed iterated function
  systems   Feng and Wang showed that two homogeneous iterated function systems in
$\mathbb{R}$ with multiplicatively independent contraction ratios necessarily
have different attractors. In this paper, we extend this result to graph
directed iterated function systems in $\mathbb{R}^n$ with contraction ratios
that are of the form $\frac{1}{\beta}$, for integers $\beta$. By using a result
of Boigelot et al., this allows us to give a proof of a conjecture of
Adamczewski and Bell. In doing so, we link the graph directed iterated function
systems to B\"uchi automata. In particular, this link extends to real numbers
$\beta$. We introduce a logical formalism that permits to characterize sets of
$\mathbb{R}^n$ whose representations in base $\beta$ are recognized by some
B\"uchi automata. This result depends on the algebraic properties of the base:
$\beta$ being a Pisot or a Parry number. The main motivation of this work is to
draw a general picture representing the different frameworks where an analogue
of Cobham's theorem is known.

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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess
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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: stat
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: econ