An Information Theoretic Analysis of Random Number Generator based on Cellular Automaton

Abstract

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.