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DMTCS
2003

On the Monotonic Computability of Semi-computable Real Numbers

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On the Monotonic Computability of Semi-computable Real Numbers
Let h : N → Q be a computable function. A real number x is h-monotonically computable (h-mc, for short) if there is a computable sequence (xs) of rational numbers which converges to x in such a way that the ratios of the approximation errors are bounded by h. In this paper we discuss the h-monotonic computability of semi-computable real numbers which are limits of monotone computable sequences of rational numbers. Especially, we show a sufficient and necessary condition for the function h such that the h-monotonic computability is simply equivalent to the normal computability.
Xizhong Zheng, George Barmpalias
Added 31 Oct 2010
Updated 31 Oct 2010
Type Conference
Year 2003
Where DMTCS
Authors Xizhong Zheng, George Barmpalias
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