Curves that must be retraced

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Curves That Must Be Retraced

We exhibit a polynomial time computable plane curve Γ 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 Γ and every positive integer n, there is some positive-length subcurve of Γ that f retraces at least n times. In contrast, every computable curve of finite length that does not int...

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ژورنال

عنوان ژورنال: Information and Computation

سال: 2011

ISSN: 0890-5401

DOI: 10.1016/j.ic.2011.01.004