Abstract
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 (x s) 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 |x i − x j| ≥ 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.
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Zheng, X. (2003). On the Divergence Bounded Computable Real Numbers. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_12
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DOI: https://doi.org/10.1007/3-540-45071-8_12
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