Timed automata were introduced by R. Alur and D. Dill as an operational model of real-time systems. In their simplest form timed automata extend classical finite automata, having only finitely many control states, by clock variables ranging over the non-negative real numbers (continuous time). Constraints on the values of the clock variables serve as guards of the transitions and as invariants in the control states. Timed automata can be combined into networks by using parallel composition and restriction operators of process algebras like CCS or CSP. One of the most important results on timed automata is that it is decidable whether a given control state is reachable. This led to the development of several tools for the automatic verification of behavioural properties of timed automata. Here we shall present in more detail the tool UPPAAL.

Timed automata

Timed automata engage in transitions from locations to locations when certain timing conditions are satisfied. These transitions either perform input and output actions on channels that will synchronise with other timed automata working in parallel or they perform internal actions that are invisible from the outside.

As a first contact with timed automata let us look at an example.

Example 4.1 (Light controller)

We wish to model a light controller with the following behaviour. Initially, the light is off. When the switch is pressed once, the light goes on (into a dim mode). If the switch is pressed twice quickly the light gets bright. Otherwise, if the switch is pressed only after a while the light goes off again.