Recursively enumerable sets and degrees
Recursively enumerable sets and degrees
Computable approximations of reals: an information-theoretic analysis
Fundamenta Informaticae
Weakly computable real numbers
Journal of Complexity
A characterization of c.e. random reals
Theoretical Computer Science
The Degree of Unsolvability of a Real Number
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
A hierarchy of Turing degrees of divergence bounded computable real numbers
Journal of Complexity
A computability theory of real numbers
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
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For any function h: N → N, we call a real number x h- bounded computable (h-bc for short) if there is a computable sequence (xs) of rational numbers which converges to x such that, for any n ∈ N, there are at most h(n) pairs of non-overlapped indices (i, j) with |xi - xj| ≥ 2-n. In this paper we investigate h-bc real numbers for various functions h. We will show a simple sufficient condition for class of functions such that the corresponding h-bc real numbers form a field. Then we prove a hierarchy theorem for h-bc real numbers. Besides we compare the semi-computability and weak computability with the h- bounded computability for special functions h.