OASIcs.CCA.2009.2269.pdf
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On Oscillation-free epsilon-random Sequences II
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6th International Conference on Computability and Complexity in Analysis (CCA'09) (CCA 2009)
Series: Open Access Series in Informatics (OASIcs) - License:
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
- Publication Date: 2009-11-25
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Jöran Mielke and Ludwig Staiger. On Oscillation-free epsilon-random Sequences II. In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 173-184, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/OASIcs.CCA.2009.2269
https://doi.org/10.4230/OASIcs.CCA.2009.2269
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.
Keywords
- Omega-words
- partial randomness
- a priori complexity
- monotone complexity
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