One of the achievements of modern science has been the realization that very few things in the world are completely static. The behaviour of many systems, both organic and synthetic, is influenced greatly by environmental changes. This interaction between a system and its environment can be vastly complicated and yet it is an area that we must try to understand if we are going to be in a position to predict the behaviour of the system and its effect on its environment.

The particular type of analysis that we present here is based on techniques that are generally referred to as algebraic. In some cases we will draw on established algebraic results but in general it is a new type of algebra that has arisen from a desire to understand the behaviour of a system in an environment. This is perhaps the most refreshing aspect of the theory. Here, for a change, is a subject whose motivation can be linked to very real problems in the modern world, a subject that has a short but dramatic history and one which has played a large role in the development of the fundamentals of computer science. However its achievements have not been restricted to this case alone and we hope to illustrate this when we examine the examples at the end of this chapter.

In many of the systems environmental changes alter the behaviour of the system and these changes in behaviour then affect the environment in some way.