A Finite-State Machine (FSM) or Finite-State Automaton is a mathematical model of computation that is used to design algorithms. It is an 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. Finite-state machines are of two types—deterministic finite-state machines and non-deterministic finite-state machines.

FSMs are used in various fields such as computer science, mathematics, engineering, and other professions to describe a mathematical model for any system that has a limited number of conditional states of being. They are used to represent sequential circuits in an abstract way. FSMs can be implemented through software or hardware to simplify a complex problem. Within an FSM, all states in consideration exist in a finite list and the abstract machine can only take on one of those states at a time. This approach allows each input and output scenario to be studied and tested.

FSMs can be used to model various systems such as vending machines, traffic lights, elevators, alarm clocks, and microwaves. They can also be used to model business processes. FSMs can be implemented using different models such as Mealy and Moore models. The Mealy model uses input actions, i.e., output depends on input and state, and leads often to a reduction of the number of states. The Moore model uses only entry actions, i.e., output depends only on state, and has the advantage of simplifying the behavior.