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Do stronger definitions of randomness exist?

✍ Scribed by Bruno Durand; Vladimir Kanovei; Vladimir A. Uspensky; Nikolai Vereshchagin


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
122 KB
Volume
290
Category
Article
ISSN
0304-3975

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✦ Synopsis


In this paper, we investigate reÿned deÿnition of random sequences. Classical deÿnitions (Martin-L of tests of randomness, uncompressibility, unpredictability, or stochasticness) make use of the notion of algorithm. We present alternative deÿnitions based on set theory and explain why they depend on the model of ZFC that is considered. We also present a possible generalization of the deÿnition when small inÿnite regularities are allowed.


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