ECCC-Report TR11-074https://eccc.weizmann.ac.il/report/2011/074Comments and Revisions published for TR11-074en-usWed, 06 Jan 2016 13:36:12 +0200
Revision 1
| Constructive dimension and Hausdorff dimension: the case of exact dimension |
Ludwig Staiger
https://eccc.weizmann.ac.il/report/2011/074#revision1The 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 $\le\alpha$ to the
case of exact dimension.Wed, 06 Jan 2016 13:36:12 +0200https://eccc.weizmann.ac.il/report/2011/074#revision1
Paper TR11-074
| Exact constructive dimension |
Ludwig Staiger
https://eccc.weizmann.ac.il/report/2011/074The 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 $\le\alpha$ to the
case of exact dimension.Thu, 05 May 2011 01:39:00 +0300https://eccc.weizmann.ac.il/report/2011/074