Language, Life, Limits

Volume 8493 of the series Lecture Notes in Computer Science pp 245-254

Function Spaces for Second-Order Polynomial Time

  • Akitoshi KawamuraAffiliated withDepartment of Computer Science, University of Tokyo
  • , Arno PaulyAffiliated withClare College, University of Cambridge

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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.


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