Kolmogorov complexity and Hausdorff dimension
Information and Computation
Proceedings of the 30th IEEE symposium on Foundations of computer science
Correspondence Principles for Effective Dimensions
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Gales and the Constructive Dimension of Individual Sequences
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
The dimensions of individual strings and sequences
Information and Computation
Correspondence Principles for Effective Dimensions
Theory of Computing Systems
Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
Refined Bounds on Kolmogorov Complexity for ω-Languages
Electronic Notes in Theoretical Computer Science (ENTCS)
Constructive dimension and Hausdorff dimension: the case of exact dimension
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
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Exact constructive dimension as a generalisation of Lutz's [10,11] approach to constructive dimension was recently introduced in [19]. It was shown that it is in the same way closely related to a priori complexity, a variant of Kolmogorov complexity, of infinite sequences as their constructive dimension is related to asymptotic Kolmogorov complexity. The aim of the present paper is to extend this to the results of [8,9,18] (see also [2, Section 13.6]) where it is shown that the asymptotic Kolmogorov complexity of infinite sequences in $\Sigma_{2}^{0}$-definable sets is bounded by their Hausdorff dimension. Using Hausdorff's original definition one obtains upper bounds on the a priori complexity functions of infinite sequences in $\Sigma_{2}^{0}$-definable sets via the exact dimension of the sets.