If you want to know the details, you should read the article more thoroughly. There is no back-propagation (or any training) involved, as this article is about what kinds of things neural networks can do in principle. I.e. how we can be sure that neural networks can in theory solve some problem we have. In practice, you have to actually find a network (by training) that solves your problem with a reasonable amount of resources, using the data you have, and that's a whole other issue (in fact, an entire research field!).
A) was focusing on functions that take a certain amount of input variables and
B) that the function (that s/he mirrored using the neural net) computes out of it directly one or more of result(s).
C) To do that s/he used a backpropagation network (which is the only model I know very well).
Right or wrong?
EDIT: when I say "directly" I mean that the function(s) does not feed itself.