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Entropy 2018, 20(12), 934; https://doi.org/10.3390/e20120934

An Informational Test for Random Finite Strings

†,‡
and
†,‡,*
Department of Computer Science, University of Verona, 37134 Verona, Italy
Current address: Strada le Grazie 15, 37134 Verona, Italy.
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 9 November 2018 / Revised: 29 November 2018 / Accepted: 3 December 2018 / Published: 6 December 2018
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Abstract

In this paper, by extending some results of informational genomics, we present a new randomness test based on the empirical entropy of strings and some properties of the repeatability and unrepeatability of substrings of certain lengths. We give the theoretical motivations of our method and some experimental results of its application to a wide class of strings: decimal representations of real numbers, roulette outcomes, logistic maps, linear congruential generators, quantum measurements, natural language texts, and genomes. It will be evident that the evaluation of randomness resulting from our tests does not distinguish among the different sources of randomness (natural, or pseudo-casual). View Full-Text
Keywords: algorithmic information theory; incompressibility; typicality; randomness test; pseudo-random generators; k-mer multiplicity; k-entropy; informational indexes algorithmic information theory; incompressibility; typicality; randomness test; pseudo-random generators; k-mer multiplicity; k-entropy; informational indexes
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Bonnici, V.; Manca, V. An Informational Test for Random Finite Strings. Entropy 2018, 20, 934.

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