TR26-034 | Limit on the computational power of $\mathrm{C}$-random strings | Alexey Milovanov

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.