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Effective fractal dimensions
Mathematical Logic Quarterly 51 (1):62-72 (2005)
Abstract
Classical fractal dimensions have recently been effectivized by characterizing them in terms of real-valued functions called gales, and imposing computability and complexity constraints on these gales. This paper surveys these developments and their applications in algorithmic information theory and computational complexity theoryMy notes
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Citations of this work
Calibrating randomness.Rod Downey, Denis R. Hirschfeldt, André Nies & Sebastiaan A. Terwijn - 2006 - Bulletin of Symbolic Logic 12 (3):411-491.
Relative Kolmogorov complexity and geometry.Stephen Binns - 2011 - Journal of Symbolic Logic 76 (4):1211-1239.
Completeness, Compactness, Effective Dimensions.Stephen Binns - 2013 - Mathematical Logic Quarterly 59 (3):206-218.
Avoiding effective packing dimension 1 below array noncomputable C.e. Degrees.Rod Downey & Jonathan Stephenson - 2018 - Journal of Symbolic Logic 83 (2):717-739.
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