A short introduction to process theory

Preface Complex computer-based systems have become an essential part of our society. These complex systems are generally composed of a number of components that act concurrently and interact with each other and the environment of the system concerned. The complexity arises to a great extent from the many ways in which the components of the system can interact. Not surprisingly , means for the description and analysis of system behaviour become increasingly important to discover flaws in computer-based systems. When it comes to description and analysis, there is advantage in treating systems, the components of which they are composed, and the environments with which they interact, on an equal footing. Therefore, we call them all processes. These lecture notes concern process theory, i.e. the theory of process behaviour, but intentionally does not cover the entire field. First of all, we do not consider all possible kinds of processes, but only a kind of frequent occurrence. In particular, we use the term process to mean any system whose behaviour is made up of discrete actions. Each action of a process is either performed synchronously with an action of another process, in which case an interaction takes place between those processes, or it is performed on its own. Moreover, we restrict ourselves to basic concepts for the description of process behaviour. More concretely, we focus in these lecture notes on the concept of a (labelled) transition system, a concept first introduced in [12]. The reason for this is twofold. Firstly, the concept of a transition system can be considered to be the fundamental concept for the description of process behaviour. Almost all formalisms meant for the description of process behaviour are based on the concept of a transition system (see e.g. [16, 9, 10]). Secondly, although mathematically simple, transition systems can model virtually all relevant properties of processes. The transition system describing the behaviour of a process is generally a suitable basis for checking properties of that process (see e.g. [2]). These lecture notes are organized in six chapters and an appendix in which the desirable background in elementary set theory is shortly reviewed. iv Preface Chap. 1, which is an introductory chapter, is primarily meant to acquire a good insight into the concept of a transition system and its relevance to the description of process behaviour. No attention is paid in this chapter to issues material to the application of transition …