No abstract

Abstract-The problem of finding satisfying assignments for conjunctive normal formula with K literals in each clause, known as K-SAT, has attracted many attentions in the previous three decades. Since it is known as NP-Complete Problem, its effective solution (finding solution within polynomial time) would be of great interest due to its relation with the most well-known open problem in computer science (P=NP Conjecture). Different strategies have been developed to solve this problem but in all of them the complexity is preserved in NP class. In this paper, by considering the recent approach of applying statistical physic methods for analyzing the phase transition in the complexity of algorithms used for solving K-SAT, we try to compute the complexity of using randomized algorithm for finding the solution of K-SAT in more relaxed regions. It is shown how the probability of literal flipping process can change the complexity of algorithm substantially. An information theoretic interpretation of this reduction in time complexity will be argued.

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.