Abstract
Realization of Randomness had always been a controversial concept with great importance both from theoretical and practical Perspectives. This realization has been revolutionized in the light of recent studies especially in the realms of Chaos Theory, Algorithmic Information Theory and Emergent behavior in complex systems. We briefly discuss different definitions of Randomness and also different methods for generating it. The connection between all these approaches and the notion of Normality as the necessary condition of being unpredictable would be discussed. Then a complex-system-based Random Number Generator would be introduced. We will analyze its paradoxical features (Conservative Nature and reversibility in spite of having considerable variation) by using information theoretic measures in connection with other measures. The evolution of this Random Generator is equivalent to the evolution of its probabilistic description in terms of probability distribution over blocks of different lengths. By getting the aid of simulations we will show the ability of this system to preserve normality during the process of coarse graining.
Highlights
TO RANDOMNESSRealization of randomness has great importance both from theoretical and practical perspective
The third family of generators for generating randomness is called Pseudo-Random Number Generators (PRNG) in which arithmetical methods are used in order to produce randomness
The work of this Random Generator can be analyzed from different perspectives such as the Conservation of initial information during the evolution leads to reversible dynamic, the intrinsic parallelism, the efficient use of initial randomness and the ability of generating acceptable number of sequences which are equivalent to the initial configuration considering their randomness or their entropy rate
Summary
Realization of randomness has great importance both from theoretical and practical perspective. Von Mises [3] was the first person who tried to define randomness mathematically based on an intuitive aspect of unpredictability He described randomness as an inability to predict the elements of an infinite binary sequence over with probability better than while the elements in the string are chosen randomly. The notion of randomness is measured in its modern formulation for finite objects by Kolmogorov complexity [10], [11] which is the result of Solmonof, Kolmogorov and Chaitins theory [12] and for infinite objects by the Mrtin-Lof measure of randomness [13], [14]. These measures are used to analyze our inhomogeneous ECA60 as a Random Generator in Section 5 and in Section 6, concluding remarks will be presented
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