Kolmogorov complexity and Hausdorff dimension
Information and Computation
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
Visualization 2001 Conference (Acm
Visualization 2001 Conference (Acm
Refined Bounds on Kolmogorov Complexity for ω-Languages
Electronic Notes in Theoretical Computer Science (ENTCS)
On Oscillation-free ε-random Sequences
Electronic Notes in Theoretical Computer Science (ENTCS)
Constructive dimension equals Kolmogorov complexity
Information Processing Letters
The extent and density of sequences within the minimal-program complexity hierarchies
Journal of Computer and System Sciences
On oscillation-free chaitin h-random sequences
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
A correspondence principle for exact constructive dimension
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
| Hi-index | 0.00 |
The present paper generalises results by Lutz and Ryabko. We prove a martingale characterisation of exact Hausdorff dimension. On this base we introduce the notion of exact constructive dimension of (sets of) infinite strings. Furthermore, we generalise Ryabko's result on the Hausdorff dimension of the set of strings having asymptotic Kolmogorov complexity = a to the case of exact dimension.