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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.16261 |
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| _version_ | 1866913146081378304 |
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| author | Milovanov, Alexey |
| author_facet | Milovanov, Alexey |
| contents | We construct a universal decompressor $U$ for plain Kolmogorov complexity $\mathrm{C}_U$ such that the Halting Problem cannot be decided by any polynomial-time oracle machine with access to the set of random strings $R_{\mathrm{C}_U} = \{x : \mathrm{C}_U(x) \ge |x|\}$. This result resolves a problem posed by Eric Allender regarding the computational power of Kolmogorov complexity-based oracles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16261 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Limit on the computational power of $\mathrm{C}$-random strings Milovanov, Alexey Computational Complexity We construct a universal decompressor $U$ for plain Kolmogorov complexity $\mathrm{C}_U$ such that the Halting Problem cannot be decided by any polynomial-time oracle machine with access to the set of random strings $R_{\mathrm{C}_U} = \{x : \mathrm{C}_U(x) \ge |x|\}$. This result resolves a problem posed by Eric Allender regarding the computational power of Kolmogorov complexity-based oracles. |
| title | Limit on the computational power of $\mathrm{C}$-random strings |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2605.16261 |