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DOI: 10.4230/OASIcs.CCA.2009.2267
URN: urn:nbn:de:0030-drops-22674
URL: https://drops.dagstuhl.de/opus/volltexte/2009/2267/
Gu, Xiaoyang ; Lutz, Jack H. ; Mayordomo, Elvira
Contributed Papers
Curves That Must Be Retraced
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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 | |
| Seminar: | 6th International Conference on Computability and Complexity in Analysis (CCA'09) | |
| Issue date: | 2009 | |
| Date of publication: | 25.11.2009 |
