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A Computability Theory of Real Numbers

  • Conference paper
Logical Approaches to Computational Barriers (CiE 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3988))

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Abstract

In mathematics, various representations of real numbers have been investigated. Their standard effectivizations lead to equivalent definitions of computable real numbers. For the primitive recursive level, however, these effectivizations are not equivalent any more. Similarly, if the weaker computability is considered, we usually obtain different weak computability notions of reals according to different representations of real number. In this paper we summarize several recent results about weak computability of real numbers and their hierarchies.

This work is supported by DFG (446 CHV 113/240/0-1) and NSFC (10420130638).

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Author information

Authors and Affiliations

  1. Department of Computer Science, Jiangsu University, Zhenjiang, 212013, China

    Xizhong Zheng

  2. Theoretische Informatik, BTU Cottbus, D-03044, Cottbus, Germany

    Xizhong Zheng

Authors
  1. Xizhong Zheng
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Swansea University, Singleton Park, SA2 8PP, Swansea, United Kingdom

    Arnold Beckmann

  2. Department of Computer Science, University of Wales Swansea, Singleton Park, SA2 8PP, Swansea, UK

    Ulrich Berger

  3. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, Amsterdam, TV, The Netherlands

    Benedikt Löwe

  4. School of Physical Sciences, Swansea University, Singleton Park, SA2 8PP, Swansea, Wales, United Kingdom

    John V. Tucker

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© 2006 Springer-Verlag Berlin Heidelberg

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Zheng, X. (2006). A Computability Theory of Real Numbers. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_60

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  • DOI: https://doi.org/10.1007/11780342_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35466-6

  • Online ISBN: 978-3-540-35468-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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