Abstract:
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 ≤ α to the case of exact dimension.
