Title :
On the measure of two-dimensional regions with polynomial-time computable boundaries
Author :
Ko, Ker-I ; Weihrauch, Klaus
Author_Institution :
Dept. of Comput. Sci., State Univ. of New York, Stony Brook, NY, USA
Abstract :
We study the computability of the Lebesgue measure of a two-dimensional region that has a polynomial-time computable boundary. It is shown that the two-dimensional measure of the boundary itself completely characterizes the computability of the measure of the interior region. Namely, if a polynomial-time computable, simple, closed curve has measure zero, then its interior region must have a computable measure. Conversely, if such a curve has a positive measure, then the measure of its interior region could be any positive, left r.e. real number
Keywords :
Turing machines; computability; computational complexity; Lebesgue measure; computability; interior region; polynomial-time computable; polynomial-time computable boundary; two-dimensional region; Computational geometry; Computer science; Polynomials; Turing machines;
Conference_Titel :
Computational Complexity, 1996. Proceedings., Eleventh Annual IEEE Conference on
Conference_Location :
Philadelphia, PA
Print_ISBN :
0-8186-7386-9
DOI :
10.1109/CCC.1996.507677
