Finite State Machine: A Comprehensive Definition

A Finite State Machine (FSM) is a mathematical model that represents a system or process with a finite number of states. It is a computational model used to describe the behavior of a system in response to a sequence of inputs or events. FSMs are widely used in computer science, electrical engineering, and other fields to design and analyze systems that exhibit complex behavior.

FSMs are composed of a set of states, a set of inputs, and a set of transitions. The states represent the different modes or conditions that the system can be in, while the inputs are the events or signals that trigger the system to change from one state to another. The transitions describe the rules that govern the movement of the system from one state to another.

There are two main types of FSMs: deterministic and non-deterministic. In a deterministic FSM, the next state of the system is uniquely determined by the current state and the input. In contrast, a non-deterministic FSM allows for multiple possible next states for a given input.

FSMs can be represented using a state diagram, which is a graphical representation of the states, inputs, and transitions of the system. State diagrams are useful for visualizing the behavior of a system and for designing and testing FSMs.

FSMs have many applications in computer science and engineering. They are used in digital circuits, computer networking protocols, compilers, and many other areas. FSMs are particularly useful for modeling systems with complex behavior, such as control systems, communication protocols, and user interfaces.

In summary, a Finite State Machine is a mathematical model used to describe the behavior of a system in response to a sequence of inputs or events. It is composed of a set of states, inputs, and transitions, and can be represented using a state diagram. FSMs are widely used in computer science and engineering to design and analyze complex systems.