Effective fractal dimensions

被引：28
|
作者：
Lutz, JH [1 ]
机构：
[1] Iowa State Univ, Dept Comp Sci, Ames, IA 50011 USA
来源：
MATHEMATICAL LOGIC QUARTERLY | 2005年 / 51卷 / 01期
关键词：
algorithmic information; circuit-size complexity; computational complexity; constructive dimension; entropy; gales; Hausdorff dimension; Kolmogorov complexity; martingales; packing dimension; polynomial-time degrees; random sequences; resource-bounded dimension;
D O I：
10.1002/malq.200310127
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Classical fractal dimensions (Hausdorff dimension and packing dimension) have recently been effectivized by (i) characterizing them in terms of real-valued functions called gales, and (ii) imposing computability and complexity constraints on these gales. This paper surveys these developments and their applications in algorithmic information theory and computational complexity theory.
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页码：62 / 72
页数：11
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