Kolmogorov complexity, Lovasz local lemma and critical exponents

Details Kolmogorov complexity, Lovasz local lemma and critical exponents Kolmogorov complexity, Lovasz local lemma and critical exponents

2010-09-25

arxiv.org/abs/1009.4995v1

Andrey Yu. Rumyantsev, Kolmogorov Complexity, Lov\'asz Local Lemma and Critical Exponents, Springer, Lecture Notes in Computer

Mathematics

Combinatorics

Scientific paper

D. Krieger and J. Shallit have proved that every real number greater than 1 is a critical exponent of some sequence. 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.

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