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DOI: 10.4230/OASIcs.CCA.2009.2269

On Oscillation-free epsilon-random Sequences II

Authors: Jöran Mielke and Ludwig Staiger

Published in: OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009)

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.

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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)

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@InProceedings{mielke_et_al:OASIcs.CCA.2009.2269,
  author =	{Mielke, J\"{o}ran and Staiger, Ludwig},
  title =	{{On Oscillation-free epsilon-random Sequences II}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  pages =	{173--184},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2269},
  URN =		{urn:nbn:de:0030-drops-22698},
  doi =		{10.4230/OASIcs.CCA.2009.2269},
  annote =	{Keywords: Omega-words, partial randomness, a priori complexity, monotone complexity}
}

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On Oscillation-free epsilon-random Sequences II

Abstract

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