Applications of State Machines

There are many applications of state machines in computer science and wider. They're primarily used for systems that change their states instantaneously between certain discreet values. Systems that change gradually, continually, are not suited for representation and programming through state machines.

Applications of state machines include language definition and analysis, game development, engineering, programming electronics with discreet inputs, evolutionary simulations, UI programming, and many more.

Think about how you could apply this to detect valid input for a compiler front-end. Or, if that interests you more, how you could use it to switch between states such as Idle, Walk, Run, Jump, etc. in a video game and swap animations along the way. Maybe you want certain parts of UI to appear differently depending on the state your user is in, so they'd maybe be less obtrusive during certain high-focus tasks or maybe some parts of your UI are mutually exclusive to avoid screen clutter - those could benefit from being implemented through a state machine. Whatever your field of interest, take some time to think about how you could apply this and tinker with it. That's the best way to learn.