Randomness relative to Cantor expansions |
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| Authors: | Cristian S. Calude Ludwig Staiger Karl Svozil |
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| Affiliation: | aDepartment of Computer Science, The University of Auckland, Private Bag 92019, Auckland, New Zealand;bMartin-Luther-Universität Halle-Wittenberg, Institut für Informatik, D-06099 Halle, Germany;cInstitut für Theoretische Physik, University of Technology Vienna, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria |
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| Abstract: | Imagine a sequence in which the first letter comes from a binary alphabet, the second letter can be chosen on an alphabet with 10 elements, the third letter can be chosen on an alphabet with 3 elements and so on. Such sequences occur in various physical contexts, in which the coding of experimental outcome varies with scale. When can such a sequence be called random? In this paper we offer a solution to the above question using the approach to randomness proposed by Algorithmic Information Theory. |
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| Keywords: | Stochastic processes Cantor expansion |
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