Cellular Automata – A Computational Point of View

The advantages of homogeneous arrays of interacting processing elements are simplicity and uniformity. It turned out that a large array of not very powerful elements operating in parallel can be programmed to be very powerful. One type of system is of particular interest: cellular automata whose homogeneously interconnected deterministic finite automata (the cells) work synchronously at discrete time steps obeying one common transition function. Cellular automata have extensively been investigated from different points of view. Here we discuss some of the main aspects from a computational point of view. The focus is on very simple types, that is, on one-dimensional cellular automata with nearest neighbor interconnections. In particular, we consider universality issues, the problem how to simulate data structures as stacks, queues, and rings without any loss of time, the famous Firing Squad Synchronization Problem, signals, and time constructible functions as well as several aspects of cellular automata as language acceptors. Some open problems are addressed.