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Admissible Representations in Computable Analysis

  • 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

Computable Analysis investigates computability on real numbers and related spaces. One approach to Computable Analysis is Type Two Theory of Effectivity (TTE). TTE provides a computational framework for non-discrete spaces with cardinality of the continuum. Its basic tool are representations. A representation equips the objects of a given space with “names”, which are infinite words. Computations are performed on these names.

We discuss the property of admissibility as a well-behavedness criterion for representations. Moreover we investigate and characterise the class of spaces which have such an admissible representation. This category turns out to have a remarkably rich structure.

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Author information

Authors and Affiliations

  1. LFCS, School of Informatics, University of Edinburgh, Edinburgh, UK

    Matthias Schröder

Authors
  1. Matthias Schröder
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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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Schröder, M. (2006). Admissible Representations in Computable Analysis. 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_48

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  • DOI: https://doi.org/10.1007/11780342_48

  • 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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