Classification of cellular automata and complexity

Cellular automata (CA) is not only a discrete dynamical system with infinite dimension, but also an important computational model. One of the most important problems in the theory of CA is how to establish the relationship between the local rules and the global behavior and then obtain the classification of CA. In this paper, we consider previous works on the classification of CA, including dynamical, statistical and computational classification and address the significance of research on theory of CA and complexity.