Revision #1 Authors: Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo

Accepted on: 19th May 2009 00:00

Downloads: 2073

Keywords:

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.

TR08-037 Authors: Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo

Publication: 24th March 2008 22:01

Downloads: 1945

Keywords:

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.