Limit on the computational power of $\mathrm{C}$-random strings

Alexey Milovanov

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arXiv · 2605.16261

Limit on the computational power of $\mathrm{C}$-random strings

Alexey Milovanov

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Abstract

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.

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BibTeX RIS

Alexey Milovanov. 2026-02-23. Limit on the computational power of $\mathrm{C}$-random strings. https://arxiv.org/abs/2605.16261

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