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DOI: 10.4230/OASIcs.CCA.2009.2273
URN: urn:nbn:de:0030-drops-22736
URL: http://drops.dagstuhl.de/opus/volltexte/2009/2273/
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Rettinger, Robert ; Zheng, Xizhong
Contributed Papers

On the Computability of Rectifiable Simple Curve (Extended Abstract)

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Abstract

In mathematics curves are defined as the images of continuous real functions defined on closed intervals and these continuous functions are called parameterizations of the corresponding curves. If only simple curves of finite lengths are considered, then parameterizations can be restricted to the injective continuous functions or even to the continuous length-normalized parameterizations. In addition, a plane curve can also be considered as a connected one-dimensional compact subset of points. By corresponding effectivizations, we will introduce in this paper four versions of computable curves and show that they are all different. More interestingly, we show also that four classes of computable curves cover even different sets of points.

BibTeX - Entry

@InProceedings{rettinger_et_al:OASIcs:2009:2273,
  author =	{Robert Rettinger and Xizhong Zheng},
  title =	{{On the Computability of Rectifiable Simple Curve (Extended Abstract)}},
  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},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2009/2273},
  URN =		{urn:nbn:de:0030-drops-22736},
  doi =		{http://dx.doi.org/10.4230/OASIcs.CCA.2009.2273},
  annote =	{Keywords: Computable curve, simple curve, rectifiable curve, point separability}
}

Keywords: Computable curve, simple curve, rectifiable curve, point separability
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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