I’d expect Turing machines to be a bad way to model this. They’re inherently blackboxy; the only “structure” they make easy to work with is function composition. The sort of structures relevant here don’t seem like they’d care much about function boundaries. (This is why I use models like these as my default model of computation these days.)
Anyway, yeah, I’m still not sure what the “relationship” should be, and it’s hard to formulate in a way that seems to capture the core idea.
I’d expect Turing machines to be a bad way to model this. They’re inherently blackboxy; the only “structure” they make easy to work with is function composition. The sort of structures relevant here don’t seem like they’d care much about function boundaries. (This is why I use models like these as my default model of computation these days.)
Anyway, yeah, I’m still not sure what the “relationship” should be, and it’s hard to formulate in a way that seems to capture the core idea.