1 - Introduction

Summary

Aims of this book

The aim of the first part of this book is to introduce three basic notions that we shall use to describe, specify and analyse reactive systems, namely

• Milner's calculus of communicating systems (CCS) (Milner, 1989),

• the model known as labelled transition systems (LTSs) (Keller, 1976), and

• Hennessy–Milner logic (HML) (Hennessy and Milner, 1985) and its extension with recursive definitions of formulae (Larsen, 1990).

We shall present a general theory of reactive systems and its applications. In particular, we intend to show the following:

1. how to describe actual systems using terms in our chosen models (i.e. either as terms in the process description language CCS or as labelled transition systems);

2. how to offer specifications of the desired behaviour of systems either as terms of our models or as formulae in HML; and

3. how to manipulate these descriptions, possibly (semi-)automatically, in order to analyse the behaviour of the model of the system under consideration.

In the second part of the book, we shall introduce a similar trinity of basic notions that will allow us to describe, specify and analyse real-time systems – that is, systems whose behaviour depends crucially on timing constraints. There we shall present the formalisms of timed automata (Alur and Dill, 1994) and timed CCS (Yi, 1990, 1991a, b) to describe real-time systems, the model of timed labelled transition systems (TLTSs) and a real-time version of Hennessy–Milner logic (Laroussinie, Larsen and Weise, 1995).