A Tight Upper Bound on Kolmogorov Complexity by Hausdorff Dimension and Uniformly Optimal Prediction (1995)
by
Ludwig Staiger
,
Rwth Aachen
| Venue: | Theory of Computing Systems |
| Citations: | 37 - 5 self |
BibTeX
@ARTICLE{Staiger95atight,
author = {Ludwig Staiger and Rwth Aachen},
title = {A Tight Upper Bound on Kolmogorov Complexity by Hausdorff Dimension and Uniformly Optimal Prediction},
journal = {Theory of Computing Systems},
year = {1995},
volume = {31},
pages = {215--229}
}
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Abstract
The present paper links the concepts of Kolmogorov complexity (in Complexity theory) and Hausdorff dimension (in Fractal geometry) for a class of recursive (computable) !-languages.
Citations
| 1412 | An introduction to Kolmogorov complexity and its applications, Second edn - Li, Vitanyi - 1997 |
| 108 | Information and Randomness — An Algorithmic Perspective - Calude - 1994 |
| 59 | Kolmogorov complexity and Hausdorff dimension - Staiger - 1993 |
| 41 | Entropy and the complexity of the trajectories of a dynamical system - Brudno - 1983 |
| 40 | Noiseless coding of combinatorial sources, Hausdorff dimension, and Kolmogorov complexity - Ryabko - 1986 |
| 16 | Algorithmic approach to the prediction problem - Ryabko - 1993 |
| 13 | The complexity and effectiveness of prediction algorithms - Ryabko - 1994 |
| 11 | Hierarchies of recursive !-languages - Staiger - 1986 |
| 7 | Combinatorial properties of the Hausdorff dimension - Staiger - 1989 |
| 2 | The Kolmogorov complexity of the real line is a fractal - Cai, Hartmanis - 1989 |
| 1 | This property, however, does not hold in general for non-closed balanced \Sigma 2 -definable !-languages, as one easily verifies. E.g. it does not hold for - Wiley - 1990 |
