Effective Hausdorff dimension
Lutz in [Lut00a] has recently proved a new characterization of Hausdorff dimension in terms of gales, which are betting strategies that generalize martingales.We present here this characterization and give three instances of how it can be used to define effective versions of Hausdorff dimension in the contexts of constructible, finite-state, and resource-bounded computation.
KeywordsCompression Ratio Hausdorff Dimension Binary Sequence Computable Function Kolmogorov Complexity
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