[lostmsu]

> I think this is easy, just make Xp sentences of the kind = "I define `randomchars()` to be this `term-in-Xc()`" and

`randomchars()` does not match your own requirement `but not that the tokens of Xp are themselves rare` and therefore is unsuitable.

[mjburgess]

good point --- so replace it with a `sample()` fn that selects from an appropriate distribution over the data

[lostmsu]

Now you have a strong statistical dependency between Xc and Xp the lack of which was required for your proof to show that the algorithm is unable to learn Xp. BTW it was already there because you already had `term-in-Xc()`.