On Time-Bounded Incompressibility of Compressible Strings and Sequences

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

On Time-Bounded Incompressibility of Compressible Strings and Sequences

Computational Complexity 2009-08-11 v4 Information Theory math.IT

Authors: E. G. Daylight , W. M. Koolen , P. M. B. Vitanyi

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.

Keywords

string algorithms

Cite

@article{arxiv.0809.2965,
  title  = {On Time-Bounded Incompressibility of Compressible Strings and Sequences},
  author = {E. G. Daylight and W. M. Koolen and P. M. B. Vitanyi},
  journal= {arXiv preprint arXiv:0809.2965},
  year   = {2009}
}

Comments

9 pages, LaTeX, no figures, submitted to Information Processing Letters. Changed and added a Barzdins-like lemma for infinite sequences with different quantification oreder, a fixed constant, and uncountably many sequences

On Time-Bounded Incompressibility of Compressible Strings and Sequences

Abstract

Keywords

Cite

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