On Time-Bounded Incompressibility of Compressible Strings and Sequences

E. G. Daylight; W. M. Koolen; P. M. B. Vitanyi

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arXiv · 0809.2965

On Time-Bounded Incompressibility of Compressible Strings and Sequences

E. G. Daylight·W. M. Koolen·P. M. B. Vitanyi

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Abstract

For every total recursive time bound $t$, a constant fraction of all compressible (low Kolmogorov complexity) strings is $t$-bounded incompressible (high time-bounded Kolmogorov complexity); there are uncountably many infinite sequences of which every initial segment of length $n$ is compressible to $\log n$ yet $t$-bounded incompressible below ${1/4}n - \log n$; and there are countable infinitely many recursive infinite sequence of which every initial segment is similarly $t$-bounded incompressible. These results are related to, but different from, Barzdins's lemma.

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E. G. Daylight, W. M. Koolen, P. M. B. Vitanyi. 2009-08-11. On Time-Bounded Incompressibility of Compressible Strings and Sequences. https://arxiv.org/abs/0809.2965

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