If S is finite, then M is a finite state machine.
I is sometimes defined so that it can be an infinite subset of S
(when of course S is infinite).
A is sometimes called the alphabet of M.
Elements in A are sometimes called events or operations.
In other models A may be infinite.
Sometimes 
is defined to be a function,
,
rather than a relation.
However, by our having be a relation, we can more easily
model nondeterminism.
Recall that it's equivalent to view the type of
as
;
thus,
given a state and an action, we can move to
possibly more than one next state.
(Aside: the action component, a, of a triple, (s, a, s'), in , is
sometimes
just viewed as the label for the state transition from s to s'. Thus, sometimes these
kinds of state machines are called labeled state transition systems.)
Applying the above definition of a state machine, we have for the Car:
Car = (
).