Divergence bounded computable real numbers |
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Authors: | Xizhong Zheng Dianchen Lu Kejin Bao |
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Affiliation: | 1. Department of Computer Science, Jiangsu University, Zhenjiang 212013, China;2. Department of Mathematics, Jiangsu University, Zhenjiang 212013, China;3. BTU Cottbus, 03044 Cottbus, Germany |
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Abstract: | A real x is called h-bounded computable , for some function h:N→N, if there is a computable sequence (xs) of rational numbers which converges to x such that, for any n∈N, at most h(n) non-overlapping pairs of its members are separated by a distance larger than 2-n. In this paper we discuss properties of h-bounded computable reals for various functions h. We will show a simple sufficient condition for a class of functions h such that the corresponding h-bounded computable reals form an algebraic field. A hierarchy theorem for h-bounded computable reals is also shown. Besides we compare semi-computability and weak computability with the h-bounded computability for special functions h. |
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Keywords: | Computability of reals Divergence bounded computability Weakly computable real Semi-computable real |
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