A Finite State Machine (FSM) is a mathematical model used in computer science and engineering to represent and control the behavior of systems that can be in a limited number of states at any given time.

It is a powerful tool for designing and analyzing systems that exhibit a finite number of possible states and transitions between those states. In an FSM, the system is represented as a set of states, along with a set of transitions between those states.

Each state represents a particular configuration or condition of the system, while each transition represents a change from one state to another under certain conditions.

The FSM can be in only one state at a time, and transitions between states are triggered by external inputs or events. FSMs are widely used in various fields, including software engineering, digital logic design, and artificial intelligence.

They are particularly useful for modeling and controlling complex systems with a finite number of possible states, such as control systems, communication protocols, and game AI. One of the key advantages of FSMs is their simplicity and clarity in representing complex systems.

They provide a clear and structured way to define the behavior of a system, making it easier to understand, analyze, and modify.

Additionally, FSMs are easy to implement in software and hardware, making them a popular choice for designing real-time systems and embedded systems. Overall, FSMs are a versatile and powerful tool for modeling and controlling systems with a finite number of states.

By using FSMs, software engineers and system designers can create efficient and reliable systems that exhibit predictable and well-defined behavior.