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

Alexey Milovanov

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

计算复杂性 2026-05-20 v2

作者: Alexey Milovanov

摘要

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.

引用

@article{arxiv.2605.16261,
  title  = {Limit on the computational power of $\mathrm{C}$-random strings},
  author = {Alexey Milovanov},
  journal= {arXiv preprint arXiv:2605.16261},
  year   = {2026}
}

备注

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 $\mathrm{C}$-random strings

摘要

引用

备注

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