arXiv Open Access 2024

On the computational power of $C$-random strings

Alexey Milovanov

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Abstrak

Denote by $H$ the Halting problem. Let $R_U: = \{ x | C_U(x) \ge |x|\}$, where $C_U(x)$ is the plain Kolmogorov complexity of $x$ under a universal decompressor $U$. We prove that there exists a universal $U$ such that $H \in P^{R_U}$, solving the problem posted by Eric Allender.

Topik & Kata Kunci

cs.CC

Penulis (1)

Alexey Milovanov

Format Sitasi

APA MLA BibTeX

Milovanov, A. (2024). On the computational power of $C$-random strings. https://arxiv.org/abs/2409.04448

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Informasi Jurnal

Tahun Terbit: 2024
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓