[ubershmekel]

Is this equivalent to each node representing a memory state?

Seems like it would not solve rtkwe's concern. In their example using tuples make a node state equal (S, COUNT_OF_DAYS), (R, COUNT_OF_DAYS)? You would still need an infinite amount of nodes to represent an infinite precision integer state.

[ColinWright]

You don't store count count of days, each node is the sequence of the previous k states. Usually k=1, but set k=2 and you get something where each state is predicted based on the previous 2 states.

So no, you don't need an infinite amount of memory, it's all still finite (although rapidly gets large).