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

Alexey Milovanov

paper

Limit on the computational power of $C$ -random strings

arXiv:2605.16261

Abstract

We construct a universal decompressor $U$ for plain Kolmogorov complexity $C_{U}$ such that the Halting Problem cannot be decided by any polynomial-time oracle machine with access to the set of random strings $R_{C_{U}} = {x : C_{U} (x) \geq ∣ x ∣}$ . This result resolves a problem posed by Eric Allender regarding the computational power of Kolmogorov complexity-based oracles.

37 pages; This paper provides the final solution to Open Problem 10 from the SIGACT News Complexity Theory Column (March 2023). Reference to the solution is available on Prof. Eric Allender's homepage:https://people.cs.rutgers.edu/~allender/publications/complete_list.html

Limit on the computational power of C-random strings

Abstract

Limit on the computational power of $C$ -random strings