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Conference on Computability in Europe

CiE 2014: Language, Life, Limits pp 245–254Cite as

Function Spaces for Second-Order Polynomial Time

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8493))

Abstract

In the context of second-order polynomial-time computability, we prove that there is no general function space construction. We proceed to identify restrictions on the domain or the codomain that do provide a function space with polynomial-time function evaluation containing all polynomial-time computable functions of that type.

As side results we show that a polynomial-time counterpart to admissibility of a representation is not a suitable criterion for natural representations, and that the Weihrauch degrees embed into the polynomial-time Weihrauch degrees.

A full version containing the omitted proofs is available on the arXiv as [18].

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Tokyo, Japan

    Akitoshi Kawamura

  2. Clare College, University of Cambridge, United Kingdom

    Arno Pauly

Authors
  1. Akitoshi Kawamura
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  2. Arno Pauly
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Editor information

Editors and Affiliations

  1. College of Science, Department of Computer Science, Swansea University, SA2 8PP, Swansea, UK

    Arnold Beckmann

  2. Department of Algorithms and Their Applications, Eötvös Loránd University, Pázmány Péter sétány 1/c,, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  3. Computer Science Institute, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, Germany

    Klaus Meer

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Kawamura, A., Pauly, A. (2014). Function Spaces for Second-Order Polynomial Time. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds) Language, Life, Limits. CiE 2014. Lecture Notes in Computer Science, vol 8493. Springer, Cham. https://doi.org/10.1007/978-3-319-08019-2_25

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  • DOI: https://doi.org/10.1007/978-3-319-08019-2_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08018-5

  • Online ISBN: 978-3-319-08019-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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