Robustness of non-computability
Logic
2021-10-01 v1 Logic in Computer Science
Abstract
Turing computability is the standard computability paradigm which captures the computational power of digital computers. To understand whether one can create physically realistic devices which have super-Turing power, one needs to understand whether it is possible to obtain systems with super-Turing capabilities which also have other desirable properties such as robustness to perturbations. In this paper we introduce a framework for analyzing whether a non-computability result is robust over continuous spaces. Then we use this framework to study the degree of robustness of several non-computability results which involve the wave equation, differentiation, and basins of attraction.
Cite
@article{arxiv.2109.15080,
title = {Robustness of non-computability},
author = {Daniel S. Graça and Ning Zhong},
journal= {arXiv preprint arXiv:2109.15080},
year = {2021}
}