Assume that for some α < 1 and for all nutural n a set F n 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. © Springer-Verlag Berlin Heidelberg 2006.
CITATION STYLE
Rumyantsev, A. Y., & Ushakov, M. A. (2006). Forbidden substrings, Kolmogorov complexity and almost periodic sequences. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3884 LNCS, pp. 396–407). Springer Verlag. https://doi.org/10.1007/11672142_32
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