The Frequent Paucity of Trivial Strings
Computational Complexity
2014-05-08 v2
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.
Cite
@article{arxiv.1310.6383,
title = {The Frequent Paucity of Trivial Strings},
author = {Jack H. Lutz},
journal= {arXiv preprint arXiv:1310.6383},
year = {2014}
}