随机性缺陷之间的关系

摘要：

随机序列的概念是由Martin-Loef在1966年提出的。与此同时，他定义了所谓的随机性亏损函数，该函数显示了随机序列与非随机序列（在某种自然意义上）的接近程度。其他亏函数可以从莱文-施诺尔定理（Levin-Schnorr theorem）得到，该定理用柯尔莫哥洛夫复杂度（Kolmogorov complexity）描述随机性。所有这些缺陷之间的差异由对数项限定。在本文中，我们表明，一些缺陷之间的差异可以尽可能大。

英文摘要：

The notion of random sequence was introduced by Martin-Loef in 1966. At the same time he defined the so-called randomness deficiency function that shows how close are random sequences to non-random (in some natural sense). Other deficiency functions can be obtained from the Levin-Schnorr theorem, that describes randomness in terms of Kolmogorov complexity. The difference between all of these deficiencies is bounded by a logarithmic term. In this paper we show that the difference between some deficiencies can be as large as possible.

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