License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/OASIcs.CCA.2009.2267
URN: urn:nbn:de:0030-drops-22674
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2009/2267/
Go to the corresponding OASIcs Volume Portal

Gu, Xiaoyang ; Lutz, Jack H. ; Mayordomo, Elvira
Contributed Papers

Curves That Must Be Retraced

pdf-format:
Gu.2267.pdf (0.4 MB)

Abstract

We exhibit a polynomial time computable plane curve ${\bf \Gamma}$ that has finite length, does not intersect itself, and is smooth except at one endpoint, but has the following property. For every computable parametrization $f$ of ${\bf\Gamma}$ and every positive integer $m$, there is some positive-length subcurve of ${\bf\Gamma}$ that $f$ retraces at least $m$ times. In contrast, every computable curve of finite length that does not intersect itself has a constant-speed (hence non-retracing) parametrization that is computable relative to the halting problem.

BibTeX - Entry

@InProceedings{gu_et_al:OASIcs:2009:2267,
  author =	{Xiaoyang Gu and Jack H. Lutz and Elvira Mayordomo},
  title =	{{Curves That Must Be Retraced}},
  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/2009/2267},
  URN =		{urn:nbn:de:0030-drops-22674},
  doi =		{10.4230/OASIcs.CCA.2009.2267},
  annote =	{Keywords: Computable analysis, computable curve, computational complexity, Hausdorff measure, rectifiable curve}
}

Keywords: Computable analysis, computable curve, computational complexity, Hausdorff measure, rectifiable curve
Collection: 6th International Conference on Computability and Complexity in Analysis (CCA'09)
Issue Date: 2009
Date of publication: 25.11.2009

DROPS-Home | Fulltext Search | Imprint | Privacy Published by LZI