Timed automaton

Imagine you have a toy car that moves around a track but sometimes it needs to wait for a signal before it can move on. This waiting time can be represented by a clock. A timed automaton is like a toy car that moves around a track but it also has a clock that tells it when to move and when to wait.

A timed automaton is a tool used in computer science to model systems that have both logical behavior (like a normal automaton) and time-dependent behavior (like waiting for a signal or producing an output after a specific time).

The automaton consists of states, transitions, and clocks. States are like different positions on the track that the car can be in. Transitions are like the path that the car takes to move from one state to another. And clocks are like timers that tell us how long the car has been waiting or how much time has elapsed since a specific event.

Timed automata can help us verify the correctness of systems that are time-dependent by simulating the behavior of the system and checking if it meets certain properties. For example, if we were modeling a traffic light system, we could use a timed automaton to ensure that the cars always have enough time to safely pass through the intersection before the light changes.

In summary, a timed automaton is a tool used in computer science to model and verify the behavior of systems that have time-dependent behavior. It consists of states, transitions, and clocks, and helps us ensure that the system behaves correctly and safely.