Relations between randomness deficiencies

Gleb Novikov

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arXiv · 1608.08246

Relations between randomness deficiencies

Gleb Novikov

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Abstract

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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Gleb Novikov. 2016-08-29. Relations between randomness deficiencies. https://arxiv.org/abs/1608.08246

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