My response to both of you is the same.
LLMs do depend on previous events, but you say they don't because you've redefined state to include previous events. It's a circular argument. In a Markov chain, state is well defined, not something you can insert any property you want to or redefine as you wish.
It's not my fault neither of you understand what the Markov property is.
They don't because n gram orders are too small and rigid to include the history in the general case.
I think srean's comment up the thread is spot on. This current situation where the state can be anything you want it to be just does not make a productive conversation.
My point, which seems so hard to grasp for whatever reason is that In a Markov chain, state is a well defined thing. It's not a variable you can assign any property to.
LLMs do depend on the previous path taken. That's the entire reason they're so useful! And the only reason you say they don't is because you've redefined 'state' to include that previous path! It's nonsense. Can you not see the circular argument?
The state is required to be a fixed, well-defined element of a structured state space. Redefining the state as an arbitrarily large, continuously valued encoding of the entire history is a redefinition that trivializes the Markov property, which a Markov chain should satisfy. Under your definition, any sequential system can be called Markov, which means the term no longer distinguishes anything.