Intrinsically Universal Cellular Automata

This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with respect to Turing and circuit universality, we discuss construction methods for small intrinsically universal cellular automata before discussing techniques for proving non universality

Evolutionary Synthesis of Cellular Automata

Synthesis of cellular automata is an important area of modeling and describing complex systems. Large amounts of combinations and candidate solutions render the usage of deterministic approaches impractical and thus nondeterministic optimization methods have to be employed. Two of the typical evolutionary approaches to synthesizing cellular automata are the evolution of a single automaton and a genetic algorithm that evolves a population of automata. The first approach, with addition of some heuristics, is known as the cellular programming algorithm. In this paper we address the second approach and develop a genetic algorithm that evolves a population of cellular automata. We test both approaches on the density classification task, which is one of the most widely studied computational problems in the context of evolving cellular automata. Comparison of the synthesized cellular automata demonstrates unexpected similarity of the evolved rules and comparable classification accuracy performance of both approaches

Cellular Automata and Randomization: A Structural Overview

The chapter overviews the methods, algorithms, and architectures for random number generators based on cellular automata, as presented in the scientific literature. The variations in linear and two-dimensional cellular automata model and their features are discussed in relation to their applications as randomizers. Additional memory layers, functional nonuniformity in space or time, and global feedback are examples of such variations. Successful applications of cellular automata random number/signal generators (both software and hardware) reported in the scientific literature are also reviewed. The chapter includes an introductory presentation of the mathematical (ideal) model of cellular automata and its implementation as a computing model, emphasizing some important theoretical debates regarding the complexity and universality of cellular automata