Finite-state Machine - Example: A Turnstile

Example: A Turnstile

An example of a very simple mechanism that can be modeled by a state machine is a turnstile. A turnstile, used to control access to subways and amusement park rides, is a gate with three rotating arms at waist height, one across the entryway. Initially the arms are locked, barring the entry, preventing customers from passing through. Depositing a coin or token in a slot on the turnstile unlocks the arms, allowing them to rotate by one-third of a complete turn, allowing a single customer to push through. After the customer passes through, the arms are locked again until another coin is inserted.

The turnstile has two states: Locked and Unlocked. There are two inputs that affect its state: putting a coin in the slot (coin) and pushing the arm (push). In the locked state, pushing on the arm has no effect; no matter how many times the input push is given it stays in the locked state. Putting a coin in, that is giving the machine a coin input, shifts the state from Locked to Unlocked. In the unlocked state, putting additional coins in has no effect; that is, giving additional coin inputs does not change the state. However, a customer pushing through the arms, giving a push input, shifts the state back to Locked.

The turnstile state machine can be represented by a state transition table, showing for each state the new state and the output (action) resulting from each input

It can also be represented by a directed graph called a state diagram (above). Each of the states is represented by a node (circle). Edges (arrows) show the transitions from one state to another. Each arrow is labeled with the input that triggers that transition. Inputs that don't cause a change of state (such as a coin input in the Unlocked state) are represented by a circular arrow returning to the original state. The arrow into the Locked node from the black dot indicates it is the initial state.