禁忌子串、Kolmogorov复杂度和概周期序列
Forbidden substrings, Kolmogorov complexity and almost periodic sequences
摘要：
假设对于某些$α<1$和对于所有自然$n$，最多$2^{αn}$“禁止的”长度为$n$的二进制串的集合$F_n$是固定的。然后存在一个无限二进制序列$ω$，它没有（长）禁止子串。我们证明了这一组合语句翻译成一个关于Kolmogorov复杂性的声明，并比较这个证明与组合的基础上Laslo Lovasz局部引理。然后我们构造了一个具有相同性质的概周期序列（从而结合了Levin和Muchnik-Semenov-Ushakov的结果）.组合证明和Kolmogorov复杂性论证都可以推广到多维情况。
英文摘要：
Assume that for some $α<1$ and for all nutural $n$ a set $F_n$ of at most $2^{αn}$ "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 proof 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 of Levin and Muchnik-Semenov-Ushakov). Both the combinatorial proof and Kolmogorov complexity argument can be generalized to the multidimensional case.
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