I think you missed my point, which is this: the first sentence in the paper's abstract is wrong.
My examples with pairs and n-tuples are also distributions.
That's a good point, and that may well be what the authors meant.
Since all PRNGs are periodic (at least all I now of), the definition eventually breaks down. I can see how it can be made to work with a bit of extra formalism, though.
Thanks.
same for 3-tuples, 4-tuples, ..., and n-tuples.
There's probably other, more sophisticated tests as well, but I'm not an expert.