Complexity theory of real functions
Complexity theory of real functions
Markov's constructive analysis; a participant's view
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Banach-Mazur Computable Functions on Metric Spaces
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
A sequentially computable function that is not effectively continuous at any point
Journal of Complexity
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We consider two classical computability notions for functions mapping all computable real numbers to computable real numbers. It is clear that any function that is computable in the sense of Markov, i.e., computable with respect to a standard G枚del numbering of the computable real numbers, is computable in the sense of Banach and Mazur, i.e., it maps any computable sequence of real numbers to a computable sequence of real numbers. We show that the converse is not true. This solves a long-standing open problem; see Kushner [9].