Computers are used more and more to provide high-quality and reliable products and services, and to control and optimise production processes. Such computers are often embedded into the products and thus hidden to the human user. Examples are computer-controlled washing machines or gas burners, electronic control units in cars needed for operating airbags and braking systems, signalling systems for high-speed trains, or robots and automatic transport vehicles in industrial production lines.

In these systems the computer continuously interacts with a physical environment or plant. Such systems are thus called reactive systems. Moreover, common to all these applications is that the computer reactions should obey certain timing constraints. For example, an airbag has to unfold within milliseconds, not too early and not too late. Reactive systems with such constraints are called real-time systems. They often appear in safety-critical applications where a malfunction of the controller will cause damage and risk the lives of people. This is immediately clear for all applications in the transport sector where computers control cars, trains and planes.

Therefore the design of real-time systems requires a high degree of precision. Here formal methods based on mathematical models of the system under design are helpful. They allow the designer to specify the system at different levels of abstraction and to formally verify the consistency of these specifications before implementing them. In recent years significant advances have been made in the maturity of formal methods that can be applied to real-time systems.

Structure of this book

In this advanced textbook we shall present three such formal approaches:

• Duration Calculus (DC for short), a logic and calculus for specifying highlevel requirements of real-time systems;

• […]