Abstract
The notion of random sequence was introduced by Martin-Löf in [3]. In the same article 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 (Proposition 1). In this paper we show (Theorems 1 and 2) that the difference between some deficiencies can be as large as possible.
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Acknowledgements
This research was supported in part by RaCAF ANR-15-CE40-0016-01. The author thanks Alexander Shen and Mikhail Andreev for their help.
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Novikov, G. (2017). Randomness Deficiencies. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_32
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DOI: https://doi.org/10.1007/978-3-319-58741-7_32
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