On the complex behavior of simple tag systems - An experimental approach

It is a well-know fact that apparently simple systems can give rise to complex behavior. But why exactly does a given system behave in a complex manner? There are two main approaches to tackle this and other related questions. One can take on a more theoretical approach or start from a more experimental study of the behavior of such systems with the help of the computer. In this paper, the experimental approach will be applied to very small tag systems. After a discussion of some of the main theoretical results on tag systems, several results from a computer-assisted and experimental study on tag systems will be analyzed. Special attention will be given to the well-known example Post provided and studied with only 2 symbols and a deletion number v = 3. These results will be combined with some theoretical results on tag systems in order to gain more insight into the computational power of simple tag systems.