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Characteristic Properties of Majorant-Computability Over the Reals

  • M. V. Korovina
  • O. V. Kudinov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1584)

Abstract

Characteristic properties of majorant-computable real-valued functions are studied. A formal theory of computability over the reals which satisfies the requirements of numerical analysis used in Computer Science is constructed on the base of the definition of majorant-computability proposed in [13]. A model-theoretical characterization of majorant-computability real-valued functions and their domains is investigated. A theorem which connects the graph of a majorant-computable function with validity of a finite formula on the set of hereditarily finite sets on \({\bar{\mathbb{R} }}\), \({\rm\bf HF}({\bar{\mathbb{R} }})\) (where \({\bar{\mathbb{R} }}\) is a proper elementary enlargement of the standard reals) is proven. A comparative analysis of the definition of majorant-computability and the notions of computability earlier proposed by Blum et al., Edalat, Sünderhauf, Pour-El and Richards, Stoltenberg-Hansen and Tucker is given. Examples of majorant-computable real-valued functions are presented.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • M. V. Korovina
    • 1
  • O. V. Kudinov
    • 2
  1. 1.Insitute of Informatics SystemsNovosibirskRussia
  2. 2.Institute of MathematicsNovosibirskRussia

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