有一个深度 1 般集

arXiv - MATH - Logic Pub Date : 2024-09-01 DOI:arxiv-2409.00631

Ang Li

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引用次数: 0

摘要

如果对任何可计算的时间边界而言，无限二元序列的时间边界无前缀科尔莫哥罗夫复杂度与其初始段的无前缀科尔莫哥罗夫复杂度之间的差值最终是无边界的，那么这个序列就是贝内特深度序列。众所周知，弱 2 代集是浅集，即不深集。在本文中，我们将证明存在一个深度 1 代集。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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There is a deep 1-generic set

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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arXiv - MATH - Logic

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