Complexity of deep computations via topology of function spaces
Logic
2026-02-19 v4 General Topology
Abstract
We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of model theory, specifically, the concept of \emph{independence} from Shelah's classification theory, to translate between topology and computation. We use the theory of Rosenthal compacta to characterize approximablility of deep computations, both deterministically and probabilistically.
Cite
@article{arxiv.2601.00528,
title = {Complexity of deep computations via topology of function spaces},
author = {Eduardo Dueñez and José Iovino and Tonatiuh Matos-Wiederhold and Luciano Salvetti and Franklin D. Tall},
journal= {arXiv preprint arXiv:2601.00528},
year = {2026}
}