License
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://drops.dagstuhl.de/opus/volltexte/2009/2267/
Gu, Xiaoyang ; Lutz, Jack H. ; Mayordomo, Elvira
Contributed Papers

Curves That Must Be Retraced

pdf-format:
Dokument 1.pdf (392 KB)

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:DSP:2009:2267,
  author =	{Xiaoyang Gu and Jack H. Lutz and Elvira Mayordomo},
  title =	{Curves That Must Be Retraced},
  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/2009/2267},
  annote =	{Keywords: Computable analysis, computable curve, computational complexity, Hausdorff measure, rectifiable curve},
}

Keywords: Computable analysis, computable curve, computational complexity, Hausdorff measure, rectifiable curve
Seminar: 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 Published by LZI