复杂镶嵌
Complex Tilings
摘要：
我们研究了具有给定瓦片集的平面的瓦片的最小复杂性。我们注意到，每个瓦片集要么不允许瓦片化，要么允许其n × n平方的具有O（n）Kolmogorov复杂度的瓦片化。我们构造的瓦片集，这个界限是紧的：所有瓦片中的所有n乘n正方形的复杂度至少为n。这增加了一个定量的角度，经典的结果非递归的平铺-我们也开发的图灵度的不可解性。关键词：Tilings，Kolmogorov复杂度，递归理论
英文摘要：
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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