Editing Finite-state machine (section)

== Example: coin-operated turnstile ==
[[File:Turnstile state machine colored.svg|thumb|upright=1.5|State diagram for a turnstile]]
[[File:Tornelli.jpg|thumb|200x200px|A turnstile]]
An example of a simple mechanism that can be modeled by a state machine is a [[turnstile]].<ref name="Koshy">{{cite book
 | last = Koshy
 | first = Thomas
 | title = Discrete Mathematics With Applications
 | publisher = Academic Press
 | year = 2004
 | pages = 762
 | url = https://books.google.com/books?id=90KApidK5NwC&pg=PA762
 | isbn = 978-0-12-421180-3}}</ref><ref name="⁇⁇⁇?">{{cite web
 |last    = Wright
 |first   = David R.
 |title   = Finite State Machines
 |work    = CSC215 Class Notes
 |publisher = David R. Wright website, N. Carolina State Univ.
 |year    = 2005
 |url    = http://www4.ncsu.edu/~drwrigh3/docs/courses/csc216/fsm-notes.pdf
 |archive-url = https://web.archive.org/web/20140327131120/http://www4.ncsu.edu/~drwrigh3/docs/courses/csc216/fsm-notes.pdf
 |url-status  = dead
 |archive-date = 27 March 2014
 |access-date = 14 July 2012
}}</ref> 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, blocking the entry, preventing patrons from passing through. Depositing a coin or [[Token coin|token]] in a slot on the turnstile unlocks the arms, allowing a single customer to push through. After the customer passes through, the arms are locked again until another coin is inserted.

Considered as a state machine, the turnstile has two possible states: ''Locked'' and ''Unlocked''.<ref name="Koshy" /> There are two possible 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. A customer pushing through the arms gives a ''push'' input and resets the state to ''Locked''.

The turnstile state machine can be represented by a [[state-transition table]], showing for each possible state, the transitions between them (based upon the inputs given to the machine) and the outputs resulting from each input:
::{| class="wikitable"
! Current State
! Input
! Next State
! Output
|-
! rowspan="2"|Locked
| coin || Unlocked || Unlocks the turnstile so that the customer can push through.
|-
| push || Locked || None
|-
! rowspan="2"|Unlocked
| coin || Unlocked || None
|-
| push || Locked || When the customer has pushed through, locks the turnstile.
|}
The turnstile state machine can also be represented by a [[directed graph]] called a [[state diagram]] ''(above)''. Each state is represented by a [[node (graph theory)|node]] (''circle''). Edges (''arrows'') show the transitions from one state to another. Each arrow is labeled with the input that triggers that transition. An input that doesn't cause a change of state (such as a ''coin'' input in the ''Unlocked'' state) is 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.