On the monotonic computability of semi-computable real numbers

Authors:
Xizhong Zheng;George Barmpalias
Affiliations:
Theoretische Informatik, Cottbus, Germany;School of Mathematics, University of Leeds, Leeds, UK
Venue:
DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
Year:
2003

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Abstract

Let h : N → Q be a computable function. A real number x is h-monotonically computable 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 the function h. In this paper we discuss the h-monotonic computability of semi-computable real numbers, i.e., 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.