There is a deep 1-generic set
<|reference_start|>There is a deep 1-generic set: 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.<|reference_end|>
@article{li2024there,
    title={There is a deep 1-generic set},
    author={Ang Li},
    journal={arXiv preprint arXiv:2409.00631},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.00631},
    primaryClass={math.LO cs.LO}
}