A finite-state machine (FSM), finite-state automaton (FSA), or simply state machine is a mathematical model of computation and 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.

In computer science, FSM are widely used in modeling of application behavior (control theory), design of hardware digital systems, software engineering, compilers, network protocols, and computational linguistics.