Finite State Machines: A Simplified Explanation

Tags: State Machines, Finite State Machines, Traffic Lights, Modeling, State Transitions

Finite State Machines (FSMs) are a key concept in computer science, and they have become increasingly popular in the world of JavaScript development. One notable library, XState, has gained a lot of attention and praise in recent times. As a senior developer, I believe it is crucial to understand FSMs and their practical applications in frontend engineering.

At a high level, a state machine is a system that can be in one of several predefined states at any given time. You may not have realized it, but state machines are all around us in the real world. Take traffic lights, for instance. A traffic light can be in one of three states: green, red, or yellow. These states determine whether vehicles should stop or go. In this case, the on/off status of the lights serves as the output, while the timer that controls the duration of each state functions as the input.

FSMs, in particular, are finite state machines that have a fixed number of states. Unlike complex systems like the world ecosystem or the life of an insect, which cannot be precisely defined in a finite number of states, FSMs like traffic lights have a limited number of states that can be easily identified and understood.

Other common examples of finite state machines include vending machines, subway entrance turnstiles, heating systems, automated subway systems, self-driving car systems, and elevators. For the purpose of this explanation, let’s continue using the traffic lights example, as it is simple and intuitive.

To model a state machine, we need to identify its states, inputs, and how they transition from one state to another. Let’s consider a traffic light with the initial state set to green. After 50 seconds, the light switches to yellow for 8 seconds, then changes to red and remains in that state for 32 seconds. Following this, it returns to the green state, and the cycle repeats indefinitely. This entire cycle lasts for 90 seconds.

We can represent this model using diagrams or state transition tables. In our case, the state transition table would look like this:

Current State	Input	Next State	Output
Green	Timer 50s	Yellow	Green light on, others off
Yellow	Timer 8s	Red	Yellow light on, others off
Red	Timer 32s	Green	Red light on, others off

It’s important to note that this example is relatively straightforward, with each state having only one logical state to transition to. However, as systems grow more complex, having such diagrams and analysis in place becomes immensely helpful in understanding how the application functions.

Let’s now explore a slightly more complex finite state machine. Imagine a house with one door, two buttons (p1 and p2), and three lights (l1, l2, and l3). By default, all the lights are turned off. Pressing either p1 or p2 turns on l1. Subsequently, pressing p1 turns off l1 and turns on l2, while pressing p2 turns off l1 and turns on l3. Pressing p1 or p2 again will turn off the currently lit light and return the system to its initial state.

We can represent this scenario with the following state transition diagram:

[Diagram: Simple House Model]

The corresponding state transition table would be:

Current State	Input	Next State
No lights turned on	p1 pressed	l1 on
No lights turned on	p2 pressed	l1 on
l1 on	p1 pressed	l2 on
l1 on	p2 pressed	l3 on
l2 on	p1 pressed	No lights turned on
l2 on	p2 pressed	No lights turned on
l3 on	p1 pressed	No lights turned on
l3 on	p2 pressed	No lights turned on

I hope this simplified explanation has made the concept of finite state machines more accessible and relatable. FSMs provide a powerful way to model and reason about complex systems, making them an invaluable tool for frontend engineers.