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Towards Computability of Higher Type Continuous Data

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New Computational Paradigms (CiE 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3526))

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Abstract

This paper extends the logical approach to computable analysis via Σ–definability to higher type continuous data such as functionals and operators. We employ definability theory to introduce computability of functionals from arbitrary domain to the real numbers. We show how this concept works in particular cases.

The authors would like to thank Klaus Weihrauch and Konstantin Korovin for useful discussions.

The first author was supported by the DFG grant N: We 843/17-1 “Berechenbare Analysis”.

The first and the second authors were partially supported by the DFG grant N:436RUS113/638, Grant Scientific School N:2112.2003.1.

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Author information

Authors and Affiliations

  1. Lehrgebiet Theoretische Informatik I, Berechenbarkeit und Logik, Fachbereich Informatik, FernUniversität in Hagen, Informatikzentrum, 58084, Hagen, Germany

    Margarita Korovina

  2. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 4 Acad. Koptyug avenue, 630090, Russia

    Margarita Korovina

  3. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Oleg Kudinov

Authors
  1. Margarita Korovina
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  2. Oleg Kudinov
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    S. Barry Cooper

  2. Department Mathematik, Universität Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany

    Benedikt Löwe

  3. Universiteit van Amsterdam,  

    Leen Torenvliet

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Korovina, M., Kudinov, O. (2005). Towards Computability of Higher Type Continuous Data. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_30

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  • DOI: https://doi.org/10.1007/11494645_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26179-7

  • Online ISBN: 978-3-540-32266-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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