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:

### 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},