Forbidden substrings, kolmogorov complexity and almost periodic sequences

Authors:
A. Yu. Rumyantsev;M. A. Ushakov
Affiliations:
Logic and algorithms theory division, Mathematics Department, Moscow State University, Russia;Logic and algorithms theory division, Mathematics Department, Moscow State University, Russia
Venue:
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Year:
2006

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Abstract

Assume that for some αn a set Fn of at most 2αn “forbidden” binary strings of length n is fixed. Then there exists an infinite binary sequence ω that does not have (long) forbidden substrings. We prove this combinatorial statement by translating it into a statement about Kolmogorov complexity and compare this proofl with a combinatorial one based on Laslo Lovasz local lemma. Then we construct an almost periodic sequence with the same property (thus combines the results from [1] and[2]). Both the combinatorial proof and Kolmogorov complexity argument can be generalized to the multidimensional case.