Journal of Symbolic Logic

Complex tilings

Bruno Durand, Leonid A. Levin, and Alexander Shen

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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.

Article information

Source
J. Symbolic Logic, Volume 73, Issue 2 (2008), 593-613.

Dates
First available in Project Euclid: 16 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1208359062

Digital Object Identifier
doi:10.2178/jsl/1208359062

Mathematical Reviews number (MathSciNet)
MR2414467

Zentralblatt MATH identifier
1141.03021

Keywords
Tilings Kolmogorov complexity recursion theory

Citation

Durand, Bruno; Levin, Leonid A.; Shen, Alexander. Complex tilings. J. Symbolic Logic 73 (2008), no. 2, 593--613. doi:10.2178/jsl/1208359062. https://projecteuclid.org/euclid.jsl/1208359062


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