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Effective fractal dimensions

Name: Effective fractal dimensions
Creator: Jack H. Lutz
Keywords: Complexity of computation (including implicit computational complexity), computational complexity, random sequences, circuit-size complexity, Kolmogorov complexity, Hausdorff dimension, constructive dimension, 0102 computer and information sciences, Algorithmic information theory, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article 25 Nov 2004Publisher:WileyJournal:Mathematical Logic Quarterly, volume 51, pages 62-72 (issn: 0942-5616, eissn: 1521-3870,

Authors: Jack H. Lutz;

doi: 10.1002/malq.200310127

Effective fractal dimensions

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Abstract

AbstractClassical 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. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Iowa State University
United States

Keywords

Complexity of computation (including implicit computational complexity), computational complexity, random sequences, circuit-size complexity, Kolmogorov complexity, Hausdorff dimension, constructive dimension, Algorithmic information theory, Algorithmic information theory (Kolmogorov complexity, etc.), gales, polynomial-time degrees, Hausdorff and packing measures, martingales, packing dimension, resource-bounded dimension, Complexity classes (hierarchies, relations among complexity classes, etc.), entropy, Theory of numerations, effectively presented structures

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