One could ask both questions, but as Cyan points out, if you know the function A of this example exactly, then you also know B exactly. What do you know about B, though, when you know A only approximately, for example, by sampling a time series? As the sample time increases beyond the autocorrelation time of A then the amount of information you get about B converges to zero, in the sense that given all of both series up to A(t) and B(t-1), the distribution of B(t) is almost identical to its unconditional distribution.

I'm sure there is a general technical definition, BTW, even though I haven't seen it. This is not a rhetorical question.