There is a deep 1-generic set
Logic
2024-09-04 v1 Logic in Computer Science
Abstract
An infinite binary sequence is Bennett deep if, for any computable time bound, the difference between the time-bounded prefix-free Kolmogorov complexity and the prefix-free Kolmogorov complexity of its initial segments is eventually unbounded. It is known that weakly 2-generic sets are shallow, i.e. not deep. In this paper, we show that there is a deep 1-generic set.
Cite
@article{arxiv.2409.00631,
title = {There is a deep 1-generic set},
author = {Ang Li},
journal= {arXiv preprint arXiv:2409.00631},
year = {2024}
}