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Effective Fractal Dimension in Algorithmic Information Theory

  • Elvira Mayordomo

Effective fractal dimension was defined by Lutz (2003) in order to quantitatively analyze the structure of complexity classes, but then interesting connections of effective dimension with information theory were also found, justifying the long existent intuition that dimension is an information content measure. Considering different bounds on computing power that range from finite memory to constructibility, including time-bounded and space-bounded computations, we review all known characterizations of effective dimension that support the thesis that effective dimensions capture what can be considered the inherent information content of a sequence in each setting.

Keywords

Compression Ratio Hausdorff Dimension Complexity Class Fractal Geometry Effective Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Elvira Mayordomo
    • 1
  1. 1.Departamento de Informática e Ingeniería de SistemasUniversidad de ZaragozaSpain

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