Gu, Xiaoyang ;
Lutz, Jack H. ;
Mayordomo, Elvira
Contributed Papers
Curves That Must Be Retraced
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 positivelength 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 constantspeed (hence nonretracing) 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 = {9783939897125},
ISSN = {21906807},
year = {2009},
volume = {11},
editor = {Andrej Bauer and Peter Hertling and KerI Ko},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2009/2267},
URN = {urn:nbn:de:0030drops22674},
doi = {http://dx.doi.org/10.4230/OASIcs.CCA.2009.2267},
annote = {Keywords: Computable analysis, computable curve, computational complexity, Hausdorff measure, rectifiable curve}
}
2009
Keywords: 

Computable analysis, computable curve, computational complexity, Hausdorff measure, rectifiable curve 
Seminar: 

6th International Conference on Computability and Complexity in Analysis (CCA'09)

Related Scholarly Article: 


Issue date: 

2009 
Date of publication: 

2009 