THE BASIC SYSTEM

In this chapter we will introduce some basic concepts of process algebra. We will do this in a modular way: first we will consider the theory BPA (Basic Process Algebra) as the kernel of all other theories that are given later. In the following sections we will show how to add some features such as deadlock, termination, projection and recursion to this theory in order to make it more powerful in its theoretical and practical applications. Each additional feature yields a conservative extension of the theories, so that we may consider the additional equations as a modular extension. Whether or not such a module should be added to the theory depends on what we want to use the theory for.

Starting in section 2.5, we consider various models for the algebraic theories that we found up to that point. Finding these models is important for more than one reason. First of all, it guarantees that the theories are consistent in the sense that the equations do not force undesirable identities to hold. Also, the models can help the intuition, they can help to visualize processes. Our models will in all cases be complete for the given theory, so the equality of two terms is true in the model exactly when it is derivable from the theory.

SYNTAX

We begin immediately with the equational specification BPA = (∑BPA, EBPA).