Function Spaces for Second-Order Polynomial Time

  • Akitoshi Kawamura
  • Arno Pauly
Conference paper

DOI: 10.1007/978-3-319-08019-2_25

Volume 8493 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
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

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.

Keywords

cartesian closed computational complexity higher order computable analysis admissible representation Weihrauch reducibility 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Akitoshi Kawamura
    • 1
  • Arno Pauly
    • 2
  1. 1.Department of Computer ScienceUniversity of TokyoJapan
  2. 2.Clare College, University of CambridgeUnited Kingdom