Add finite-state-machine topic

topics/finite-state-machine/index.md

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+---
+aliases: finite-state-machines, fsm, finite-state-automaton, finite-state-automata, finite-state-automatons, fsa, finite-automaton, finite-automata, finite-automatons, state-machine
+display_name: Finite-state machine
+related: automaton, deterministic-finite-automaton, nondeterministic-finite-automaton
+short_description: A formalism consisting of a finite set of states and a transition function describing when to move from one state to another.
+topic: finite-state-machine
+wikipedia_url: https://en.wikipedia.org/wiki/Finite-state_machine
+---
+A **finite-state machine** (FSM), **finite-state automaton** (FSA), or simply **state machine** is a mathematical [model of computation](https://en.wikipedia.org/wiki/Model_of_computation) and an [abstract machine](https://en.wikipedia.org/wiki/Abstract_machine) that can be in exactly one of a finite number of states at any given time.
+The FSM can change from one state to another in response to some inputs; the change from one state to another is called a *transition*.
+An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition.
+
+In computer science, FSM are widely used in modeling of application behavior ([control theory](https://en.wikipedia.org/wiki/Control_theory)), design of [hardware digital systems](https://en.wikipedia.org/wiki/Digital_electronics), [software engineering](https://github.com/topics/software-engineering), [compilers](https://github.com/topics/compiler), [network protocols](https://en.wikipedia.org/wiki/Network_protocol), and [computational linguistics](https://en.wikipedia.org/wiki/Computational_linguistics).