What is a state machine and how does it work?

Have you ever wondered how your favorite video game character knows when to jump, run, or attack? Or how a vending machine knows when to dispense your favorite snack? The answer lies in the concept of state machines.

A state machine is a mathematical model used to describe the behavior of a system. It consists of a set of states, transitions between those states, and actions that occur when a transition is made. In simpler terms, a state machine is like a flowchart that describes how a system should behave based on its current state.


At the heart of every state machine are states. A state is a condition or situation in which a system can exist. For example, a vending machine can be in a "ready" state, where it is waiting for a user to make a selection, or a "dispensing" state, where it is dispensing the selected item.

States can be represented graphically using circles or rectangles. Each state is given a unique name, such as "ready" or "dispensing". The current state of the system is known as the "active" state.


Transitions are the paths that a state machine can take from one state to another. They are triggered by events or conditions that occur within the system. For example, when a user selects an item from a vending machine, a transition is made from the "ready" state to the "dispensing" state.

Transitions are represented graphically using arrows. Each arrow is labeled with the event or condition that triggers the transition. For example, an arrow from the "ready" state to the "dispensing" state might be labeled "user selects item".


Actions are the things that happen when a transition is made. They can be anything from displaying a message on a screen to dispensing a product from a vending machine. Actions are associated with transitions, not states.

Actions are represented graphically using rectangles. Each rectangle is labeled with the action that occurs when the associated transition is made. For example, a rectangle associated with the transition from the "ready" state to the "dispensing" state might be labeled "dispense selected item".


Let's take a look at a simple example of a state machine. Imagine a traffic light at an intersection. The traffic light can be in one of three states: "green", "yellow", or "red". The traffic light transitions between these states based on a timer.

graph TD
    A[Green] --> B[Yellow]
    B --> C[Red]
    C --> D[Green]

In this example, the traffic light starts in the "green" state. After a certain amount of time, it transitions to the "yellow" state. After another amount of time, it transitions to the "red" state. Finally, after a third amount of time, it transitions back to the "green" state.


State machines are a powerful tool for modeling the behavior of complex systems. They allow us to describe how a system should behave based on its current state, and they provide a clear and concise way to represent that behavior graphically.

Whether you're designing a video game, building a vending machine, or controlling a traffic light, understanding state machines is essential. So the next time you're playing your favorite game or grabbing a snack from a vending machine, take a moment to appreciate the state machine that makes it all possible.

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Written by AI researcher, Haskell Ruska, PhD (haskellr@mit.edu). Scientific Journal of AI 2023, Peer Reviewed