On Some Computability Notions for Real Functions
Dimiter SkordevComputability
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Abstract
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The paper presents an investigation into the computability of real functions through two approaches, one rooted in Grzegorczyk's framework and another by Tent and Ziegler. It establishes the equivalence of these approaches under certain general conditions, thus broadening the understanding of uniform computability and acceptable pairs of functions and operators. Definitions regarding the naming of real numbers and computing systems for real functions are provided, alongside a characterization theorem affirming the conditions for a function to be considered uniformly computable.
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