## Simple Example of A Genuine Finite State Machine

## A Simple Vending Machine

A vending machine dispenses pieces of candy that cost 20 cents each. The
machine accepts nickels and dimes only and does not give change. As soon as
the amount deposited equals or exceeds 20 cents, the machine releases a piece
of candy. The next coin deposited starts the process over again. The operation
of the machine is represented by the diagram above. Each circle represents a
state of the machine: the state in which 0 cents has been deposited, 5 cents,
10 cents, 15 cents, and 20 cents or more. The unlabeled arrow pointing to
"0 cents deposited" indicates that this is the initial state of the machine.
The double circle around "20 cents or more deposited" indicates that candy is
released when the machine has reached this state. (It is called an **accepting
state** of the machine because when the machine is in this state it has
accepted the input sequence of coins as payment for candy.) the arrows that
link the states indicate what happens when a particular input is made to the
machine in each of its various states. For instance, the arrow labeled "nickel"
that goes from "0 cents deposited" to "5 cents deposited" indicates that when
the machine is in the state "0 cents deposited" and a nickel is inserted, the
machine goes to the state "5 cents deposited." The arrow labeled "dime" that
goes from "15 cents deposited" to "20 cents or more deposited" indicates that
when the machine is in the state "15 cents deposited" and a dime is inserted,
the machine goes to the state "20 cents or more deposited" and candy is
dispensed. (In this case the purchaser would pay 25 cents for the candy since
the machine does not return change.) The arrow labeled "dime" that goes from
"20 cents or more inserted" to "10 cents deposited" indicates that when the
machine is the state "20 cents or more deposited" and a dime is inserted, the
machine goes back to the state "10 cents deposited". (This corresponds to the
fact that after the machine has dispensed a piece of candy, it starts the
operation all over again)