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Complex Tilings | | Bruno Durand
; Leonid A. Levin
; Alexander Shen
; | | Date: |
4 Jul 2001 | | Subject: | Computational Complexity; Discrete Mathematics ACM-class: F.1.1; G.2.1 | cs.CC cs.DM | | Abstract: | We study the minimal complexity of tilings of a plane with a given tile set. We note that any 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 Omega(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: Tiling, Kolmogorov complexity, recursion theory. | | Source: | arXiv, cs.CC/0107008 | | Services: | Forum | Review | PDF | Favorites | |
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