Preprint Article Version 1 This version is not peer-reviewed

An Informational Test for Random Finite Strings

Version 1 : Received: 9 November 2018 / Approved: 15 November 2018 / Online: 15 November 2018 (10:37:31 CET)

A peer-reviewed article of this Preprint also exists.

Bonnici, V.; Manca, V. An Informational Test for Random Finite Strings. Entropy 2018, 20, 934. Bonnici, V.; Manca, V. An Informational Test for Random Finite Strings. Entropy 2018, 20, 934.

Journal reference: Entropy 2018, 20, 934
DOI: 10.3390/e20120934

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 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).

Subject Areas

Algorithmic Information Theory; Incompressibility; Typicality; Randomness Test; Pseudo-random Generators; k-mer Multiplicity; k-Entropy; Informational indexes

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