A Finite State Machine, or FSM, is a computation model that can be used to simulate sequential logic, or, in other words, to represent and control execution flow. Finite State Machines can be used to model problems in many fields, including mathematics, artificial intelligence, games or linguistics.

Why the term state machine is used?

State machines are used to model real-world software when the identified state must be documented along with how it transitions from one state to another.

What do you think about the importance of finite state machine in automata theory?

Finite-state machines are ideal computation models for a small amount of memory, and do not maintain memory. This mathematical model of a machine can only reach a finite number of states and transitions between these states.