English

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

R2 v1 2026-06-22T01:27:56.462Z