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.
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© 2004 Kluwer Academic Publishers
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Cámara, E.M. (2004). Effective Hausdorff dimension. In: Löwe, B., Piwinger, B., Räsch, T. (eds) Classical and New Paradigms of Computation and their Complexity Hierarchies. Trends in Logic, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2776-5_10
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DOI: https://doi.org/10.1007/978-1-4020-2776-5_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-2775-8
Online ISBN: 978-1-4020-2776-5
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