The Terms "Finite" and "State"
The "automaton" in "finite state automaton"
We now know what an automaton is. It is simply an machine that functions automatically in response to inputs of some sort.
The "state" in "finite state automaton"
It might also be clear from the examples given earlier what the term "state" means in "finite state automaton." "State" simply refers to a "state of being" in which an automaton can be. This is indicated by what the automaton remembers about the activity or computation it is currently performing. For example, in the candy bar dispenser example, one of the states of the dispenser is the state of remembering that thirty-five cents have so far been inserted.
The states of an automaton are important, because they remember the status of the automaton so far, so that the next input processed can lead the automaton to the correct next state. For example, in the candy bar dispenser, the automaton can be set correctly to the state of remembering that forty-five cents have now been inserted if a dime is inserted while the dispenser is in the state of remembering that up to this point thirty-five cents had been inserted.
The "finite" in "finite state automaton"
By attaching the adjective "finite" to the description of an automaton, we are placing a restriction on it. A finite state automaton can only have a finite number of states. That is, it can only remember a fixed number of different things about the inputs it is processing. (There are other things about finite state automata that are finite as well, which we will discover later.) The restriction to a finite number of states is pretty severe, as we will discover. However, finite state automata are still quite interesting in their own right.
