Exploring the Different Types of Finite State Machines: A Comprehensive Guide

A Finite State Machine (FSM) is a mathematical model that represents a system's behavior in terms of its states, inputs, and outputs. It's a fundamental concept in digital logic design and computer science.

States:

An FSM can be in one of a finite number of states at any given time. These states represent different conditions or situations the system can be in.

Inputs: The FSM accepts inputs (symbols or events) that trigger transitions between states.
Outputs: Depending on the current state and the received input, the FSM might generate an output (a signal or action).

FSMs are used in various applications, including:

Design of digital circuits
Modeling behavior of systems like traffic lights, vending machines, and control systems
Building stateful software components.

There are two main categories of FSMs based on their output behavior :-

Mealy Machine

Output Depends on State and Input: In a Mealy machine, the output is determined by both the current state and the current input. This means that for the same input, the output can be different depending on the starting state of the machine.

Advantages: Offers flexibility for generating diverse outputs based on the current context.
Disadvantages: Can be more complex to design and analyze due to the dependence on both state and input for output generation.

Example:

Consider a vending machine modeled as a Mealy machine. It has states like "idle," "coin inserted," and "item dispensed." The inputs could be "coin inserted," "button pressed," and "change returned." The outputs might include "dispense item," "return coin," and "play sound." Based on the current state and the input, the machine generates the appropriate output.

Moore Machine

Output Depends Only on State:

In a Moore machine, the output solely depends on the current state of the machine. The received input can trigger a state transition, but the output is based only on the new state reached.

Advantages: Simpler to design and analyze since the output depends only on the current state.
Disadvantages: May require additional states to achieve the same functionality as a Mealy machine for some applications.

Example:

Revisiting the vending machine example as a Moore machine: It would have similar states, but the outputs would depend only on the current state. For instance, the output in the "coin inserted" state might always be "play sound," regardless of whether another coin is inserted. This could be implemented with additional states for handling multiple coin insertions in a Mealy machine.

Mealy vs. Moore Machines

Feature	Mealy Machine	Moore Machine
Output depends on	Current state and current input	Current state only
Complexity	More complex	Simpler
Flexibility	More flexible for output generation	Less flexible
Design	More challenging to design	Easier to design
Applications	Well-suited for scenarios where output depends on both state and input	Suitable for simpler scenarios where output depends only on the current state