There is a deep 1-generic set

Ang Li

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arXiv · 2409.00631

There is a deep 1-generic set

Ang Li

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Abstract

An infinite binary sequence is Bennett deep if, for any computable time bound, the difference between the time-bounded prefix-free Kolmogorov complexity and the prefix-free Kolmogorov complexity of its initial segments is eventually unbounded. It is known that weakly 2-generic sets are shallow, i.e. not deep. In this paper, we show that there is a deep 1-generic set.

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BibTeX RIS

Ang Li. 2024-09-01. There is a deep 1-generic set. https://arxiv.org/abs/2409.00631

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