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June 2008 Complex tilings
Bruno Durand, Leonid A. Levin, Alexander Shen
J. Symbolic Logic 73(2): 593-613 (June 2008). DOI: 10.2178/jsl/1208359062

Abstract

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×n)-squares. We construct tile sets for which this bound is tight: all (n×n)-squares in all tilings have complexity Ω(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.

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Bruno Durand. Leonid A. Levin. Alexander Shen. "Complex tilings." J. Symbolic Logic 73 (2) 593 - 613, June 2008. https://doi.org/10.2178/jsl/1208359062

Information

Published: June 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1141.03021
MathSciNet: MR2414467
Digital Object Identifier: 10.2178/jsl/1208359062

Rights: Copyright © 2008 Association for Symbolic Logic

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Vol.73 • No. 2 • June 2008
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