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DOI: 10.4230/OASIcs.CCA.2009.2269
URN: urn:nbn:de:0030-drops-22698
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2269/
Mielke, Jöran ; Staiger, Ludwig
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:DSP:2009:2269,
  author =	{J{\"o}ran Mielke and Ludwig Staiger},
  title =	{On Oscillation-free epsilon-random Sequences II},
  booktitle =	{6th Int'l Conf. on Computability and Complexity in Analysis},
  year =	{2009},
  editor =	{Andrej Bauer and Peter Hertling and Ker-I Ko},
  publisher =	{Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2269},
  annote =	{Keywords: Omega-words, partial randomness, a priori complexity, monotone complexity},
}

Keywords: Omega-words, partial randomness, a priori complexity, monotone complexity
Seminar: 6th International Conference on Computability and Complexity in Analysis (CCA'09)
Issue date: 2009
Date of publication: 25.11.2009

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