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Revision #1 to TR08-037 | 19th May 2009 00:00

Curves That Must Be Retraced

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Revision #1
Authors: Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo
Accepted on: 19th May 2009 00:00
Downloads: 1349
Keywords: 


Abstract:

We exhibit a polynomial time computable plane curve 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 GAMMA and every positive integer n, there is some positive-length subcurve of GAMMA that f retraces at least n 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.


Paper:

TR08-037 | 29th February 2008 00:00

Curves That Must Be Retraced





TR08-037
Authors: Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo
Publication: 24th March 2008 22:01
Downloads: 1278
Keywords: 


Abstract:

We exhibit a polynomial time computable plane curve 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 GAMMA and every positive integer n, there is some positive-length subcurve of GAMMA that f retraces at least n 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.



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