On the computational power of $C$-random strings
<|reference_start|>On the computational power of $C$-random strings: Denote by $H$ the Halting problem. Let $R_U: = \{ x | C_U(x) \ge |x|\}$, where $C_U(x)$ is the plain Kolmogorov complexity of $x$ under a universal decompressor $U$. We prove that there exists a universal $U$ such that $H \in P^{R_U}$, solving the problem posted by Eric Allender.<|reference_end|>
@article{milovanov2024on,
    title={On the computational power of $C$-random strings},
    author={Alexey Milovanov},
    journal={arXiv preprint arXiv:2409.04448},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.04448},
    primaryClass={cs.CC}
}