Effective Genericity and Differentiability
Logic
2014-08-27 v2
Abstract
We prove that a real x is 1-generic if and only if every differentiable computable function has continuous derivative at x. This provides a counterpart to recent results connecting effective notions of randomness with differentiability. We also consider multiply differentiable computable functions and polynomial time computable functions.
Keywords
Cite
@article{arxiv.1309.3983,
title = {Effective Genericity and Differentiability},
author = {Rutger Kuyper and Sebastiaan A. Terwijn},
journal= {arXiv preprint arXiv:1309.3983},
year = {2014}
}
Comments
Revision: added sections 6-8; minor corrections