Kolmogorov complexity, Lovász local lemma and critical exponents

Authors:
Andrey Yu. Rumyantsev
Affiliations:
Moscow State Lomonosov University, Mathematics Dept., Logic and Algorithms Theory Division
Venue:
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
Year:
2007

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Forbidden substrings, kolmogorov complexity and almost periodic sequences

STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science

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Abstract

D. Krieger and J. Shallit have proved that every real number greater than 1 is a critical exponent of some sequence [1]. We show how this result can be derived from some general statements about sequences whose subsequences have (almost) maximal Kolmogorov complexity. In this way one can also construct a sequence that has no "approximate" fractional powers with exponent that exceeds a given value.