Time-bounded incompressibility of compressible strings and sequences

Authors:
Edgar G. Daylight;Wouter M. Koolen;Paul M. B. Vitányi
Affiliations:
University of Amsterdam, Institute of Logic, Language, and Computation, Amsterdam, The Netherlands;Centrum voor Wiskunde en Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands;Centrum voor Wiskunde en Informatica, Science Park 123, 1098 XG Amsterdam, The Netherlands and University of Amsterdam, Department of Computer Science, Amsterdam, The Netherlands
Venue:
Information Processing Letters
Year:
2009

Citing 3
Cited 0

Kolmogorov Complexity and Instance Complexity of Recursively Enumerable Sets

SIAM Journal on Computing
Computational depth: concept and applications

Theoretical Computer Science - Foundations of computation theory (FCT 2003)
An Introduction to Kolmogorov Complexity and Its Applications

An Introduction to Kolmogorov Complexity and Its Applications

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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 logn yet t-bounded incompressible below 14n-logn; and there is a countably infinite number of recursive infinite sequences of which every initial segment is similarly t-bounded incompressible. These results and their proofs are related to, but different from, Barzdins's lemma.