Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complex Tilings   We study the minimal complexity of tilings of a plane with a given tile set.
We note that every tile set admits either no tiling or some tiling with O(n)
Kolmogorov complexity of its n-by-n squares. We construct tile sets for which
this bound is tight: all n-by-n squares in all tilings have complexity at least
n. This adds a quantitative angle to classical results on non-recursivity of
tilings -- that we also develop in terms of Turing degrees of unsolvability.
  Keywords: Tilings, Kolmogorov complexity, recursion theory

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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: physics