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Kolmogorov complexity and Hausdorff dimension

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Ludwig Staiger at Martin Luther University Halle-Wittenberg
Ludwig Staiger
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Abstract

this paper we are mainly interestedin the first order approximation (i.e. the linear growth) of K(fi=\Delta). We considerthe functions
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... In particular, they allow for a definition of a non-integral notion of dimension, Hausdorff dimension. Works by Ryabko [15] [16], Staiger [20] and Cai and Hartmanis [1] established a close connection between Hausdorff dimension and the (lower) asymptotic complexity of sequences given as lim inf n K (A n )/n. Later, Lutz [7] used the martingale characterization of nullsets to define an effective variant of Hausdorff measure and dimension. ...
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