[Frost1x]

For embedded systems and game development I definitely understand automata applications (from experience) but web development has me curious. Are you writing transpilers or perhaps something else (I also try to avoid web dev, so there's that).

[learc83]

Mostly for user interfaces and modeling business processes. But I’ve also done some work on a super simple language for some of our non technical people to use for data transformation, and a templating system for form generation.

[Grimm1]

Not OP but there are more than a few domains that can be modeled with automata, a shipping pipeline with approval steps is an example.

[nitrogen]

Ecommerce order/payment/shipping status is a good example. Anything that has a well defined state that can be changed by events is well-modeled as a state machine of some kind. Also anything that has to progress through certain steps and might be interrupted or have exception cases, and you want to proceed/retry idempotently.

Personally I have also found basic graph theory to be immensely useful for representing and reasoning about things.

[learc83]

>Personally I have also found basic graph theory to be immensely useful for representing and reasoning about things.

I agree! The graph theory portion of my algorithms class (more than half of the class) was the third most useful thing I learned in my degree.