This is like saying all computers are state machines because they have finite amounts of memory and disk space. It's sort of true, but it's not a useful mathema

This is like saying all computers are state machines because they have finite amounts of memory and disk space. It's sort of true, but it's not a useful mathematical model. With a Markov chain, you're assuming a state machine where each state has independent probabilities on outgoing edges. As the number of states gets larger, you have fewer training samples for each state. When n gets large enough, nearly all states have zero training samples; they've never been seen before. How do you estimate probabilities? Better to just say it's a stateless function of the input.