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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.04448 |
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| _version_ | 1866916687016624128 |
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| author | Milovanov, Alexey |
| author_facet | Milovanov, Alexey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04448 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the computational power of $C$-random strings Milovanov, Alexey Computational Complexity 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. |
| title | On the computational power of $C$-random strings |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2409.04448 |