Function spaces for second-order polynomial time
Computational Complexity
2015-10-28 v2 Logic in Computer Science
Logic
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.
Cite
@article{arxiv.1401.2861,
title = {Function spaces for second-order polynomial time},
author = {Akitoshi Kawamura and Arno Pauly},
journal= {arXiv preprint arXiv:1401.2861},
year = {2015}
}