Is there a difference between a "finite state machine" and a "state machine"?

Question

I'm not sure I understand if there is a difference between a finite state machine and a state machine? Am I thinking about this too hard?

Answer 1

I'm not sure I understand if there is a difference between a finite state machine and a state machine? Am I thinking about this too hard?

Yes, you are thinking about it too hard. :-) It depends on context.

Obviously, taken literally, the term "finite state machine" indicates a finite number of states, while "state machine" makes no such promise. So, yes, there is a difference.

However, I think, depending on the context of the conversation, people simply say "state machine" in short-hand without consider whether they mean "finite state machine" or "state machine". And in our field of software programming, where state machines are usually represented in code, we can often use "state machine" interchangeably with "finite state machine". So, really, no, there is no difference.

OTOH, if I were talking to a mathematician after night class on campus one evening, I may be more selective about the specific terms I used. So, yes, there is a difference (in this case).

Answer 2

Sure there's a difference. One has a finite number of states, and the other has an infinite number of states. It's kind of awkward to draw an infinite state machine, but the math that permits a finite state machine will permit an infinite state machine, as well.

Take a look at the mathematical model section of the Wikipedia page of FSM's. See where it says 'S is a finite, non-empty set of states'? Erase 'finite'. Your state transition function will become infinite as well, but that's ok, there are a lot of infinite functions.

"From.ME.to.YOU" is conflating Wikipedia's verbal shorthand with a real proclamation of equality.