when quoting this document, please refer to the following
DOI:
URN: urn:nbn:de:0030-drops-22698
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Contributed Papers

### On Oscillation-free epsilon-random Sequences II

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### Abstract

It has been shown (see (Staiger, 2008)), that there are strongly \textsc{Martin-L\"of}-$\varepsilon$-random $\omega$-words that behave in terms of complexity like random $\omega$-words. That is, in particular, the \emph{a priori} complexity of these $\varepsilon$-random $\omega$-words is bounded from below and above by linear functions with the same slope $\varepsilon$. In this paper we will study the set of these $\omega$-words in terms of \textsc{Hausdorff} measure and dimension.

Additionally we find upper bounds on \emph{a priori} complexity, monotone and simple complexity for a certain class of $\omega$-power languages.

### BibTeX - Entry

@InProceedings{mielke_et_al:OASIcs:2009:2269,
author =	{J{\"o}ran Mielke and Ludwig Staiger},
title =	{{On Oscillation-free epsilon-random Sequences II}},
booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
series =	{OpenAccess Series in Informatics (OASIcs)},
ISBN =	{978-3-939897-12-5},
ISSN =	{2190-6807},
year =	{2009},
volume =	{11},
editor =	{Andrej Bauer and Peter Hertling and Ker-I Ko},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},