The Car has a finite behavior of finite executions. In general, a state machine can have infinite executions and infinite behavior. An infinite execution is an infinite sequence of alternating states and actions. An infinite behavior is an infinite set of executions. Note that elements in an infinite behavior might all be finite.
Consider a simple light switch whose interface and state transition diagram are shown below:
Light = 
.
Some executions of Light are:
There are an infinite number of finite executions and the last execution listed above is infinite. Thus Beh(Light) is an infinite set of finite and infinite traces.
Here is an example of a state machine with more than one infinite trace:
One of the infinite traces (event-based) is the infinite sequence of pressR actions. What are some others?