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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.

Any finite state PRNG has to be periodic. Good luck implementing an infinite state one.

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