4 found
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  1.  33
    Conditional Computability of Real Functions with Respect to a Class of Operators.Ivan Georgiev & Dimiter Skordev - 2013 - Annals of Pure and Applied Logic 164 (5):550-565.
    For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect to this class. These two computability notions are natural generalizations of certain notions introduced in a previous paper co-authored by Andreas Weiermann and in another previous paper by the same authors, respectively. Under certain weak assumptions about the class in question, (...)
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  2.  10
    Continued Fractions of Primitive Recursive Real Numbers.Ivan Georgiev - 2015 - Mathematical Logic Quarterly 61 (4-5):288-306.
  3.  18
    Computable Irrational Numbers with Representations of Surprising Complexity.Ivan Georgiev, Lars Kristiansen & Frank Stephan - 2021 - Annals of Pure and Applied Logic 172 (2):102893.
  4.  7
    On Subrecursive Complexity of Integration.Ivan Georgiev - 2020 - Annals of Pure and Applied Logic 171 (4):102777.
    We consider the complexity of the integration operator on real functions with respect to the subrecursive class M^2 . We prove that the definite integral of a uniformly M^2-computable analytic real function with M^2-computable limits is itself M^2-computable real number. We generalise this result to integrals with parameters and with varying limits. As an application, we show that the Euler-Mascheroni constant is M^2-computable.
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