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- W4300568148 abstract "Let $K$ denote prefix-free Kolmogorov Complexity, and $K^A$ denote it relative to an oracle $A$. We show that for any $n$, $K^{emptyset^{(n)}}$ is definable purely in terms of the unrelativized notion $K$. It was already known that 2-randomness is definable in terms of $K$ (and plain complexity $C$) as those reals which infinitely often have maximal complexity. We can use our characterization to show that $n$-randomness is definable purely in terms of $K$. To do this we extend a certain ``limsup'' formula from the literature, and apply Symmetry of Information. This extension entails a novel use of semilow sets, and a more precise analysis of the complexity of $Delta_2^0$ sets of mimimal descriptions." @default.
- W4300568148 created "2022-10-03" @default.
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- W4300568148 date "2022-08-05" @default.
- W4300568148 modified "2023-10-17" @default.
- W4300568148 title "Limit Complexities, Minimal Descriptions, and $n$-Randomness" @default.
- W4300568148 doi "https://doi.org/10.48550/arxiv.2208.02982" @default.
- W4300568148 hasPublicationYear "2022" @default.
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