You're just explaining what the word "nondeterministic" means when you put it before "finite automaton", which doesn't have much to do with what "nondeterministic" means in other places.
You're just explaining what the word "nondeterministic" means when you put it before "finite automaton", which doesn't have much to do with what "nondeterministic" means in other places.
Nondeterminism before "finite automaton" is how the concept is developed in the theory of computation, which later develops into nondeterminism before "turning machine", and eventually before "polynomial time".
You seem to be misunderstanding the role automata theory plays in the larger framework of the theory of computation. It is not a "special case" of nondeterminism, it is the foundation for how all of the theory of computation is built.
Additionally, I'm also demonstrating how that exact same concept plays out in the other framework of computation, functional programming, and it works fundamentally the same way.
I have to say it's a bit surprising to need to defend the fundamental principles of computer science on HN. The topic is "how LLMs compute things" so using the computational definition of nondeterminism seem entirely relevant.