Cellular automata make up a class of completely discrete dynamical systems, which have became a core subject in the sciences of complexity due to their conceptual simplicity, easiness of implementation for computer simulation, and their ability to exhibit a wide variety of amazingly complex behavior.

The emergence of simple patterns out of complex systems motivates the study of behavior independent of the particulars of a system. Cellular Automata is a simple tool that displays such characteristics and is therefore useful for modeling. We provide an introduction to Quantum Cellular Automata.

Contents: Algebraic preliminaries; Semigroups and beyond; Languages and automata; Recognizable and rational sets; Green's relations and local theory; Profinite words.

Employing simple yet versatile parallel cellular models, coupled with evolutionary computation techniques, this volume explores the issue of constructing man-made systems that exhibit characteristics such as those manifest by their natural counterparts.

Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship.