The Frequent Paucity of Trivial Strings

Jack H. Lutz

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arXiv · 1310.6383

The Frequent Paucity of Trivial Strings

Jack H. Lutz

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Abstract

A 1976 theorem of Chaitin can be used to show that arbitrarily dense sets of lengths n have a paucity of trivial strings (only a bounded number of strings of length n having trivially low plain Kolmogorov complexities). We use the probabilistic method to give a new proof of this fact. This proof is much simpler than previously published proofs, and it gives a tighter paucity bound.

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Jack H. Lutz. 2014-05-07. The Frequent Paucity of Trivial Strings. https://arxiv.org/abs/1310.6383

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