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Revision(s):
Revision #1 Authors: Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo
Accepted on: 19th May 2009 00:00
Downloads: 132
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: 134
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.