[OJFord]

Surely any PP problem can be done in P, it's just a matter of encoding? As in if you give me a box that computes whatever in PP, then I can give you back a box that takes a single input consisting of 1s to the length of each value delimited by 0s, turns those back into integers (linear), uses your PP box, and returns its output - but now it's polynomial in the length of my input?

(I said integers but I don't think that's significant, just a matter of encoding scheme - we can use a single 0 for decimal point and two for delimiting inputs say.)

But anyway isn't the joke that sleep-time doesn't count, because the computer could be doing something else? It's actually quite compelling in a 'this is stupid, I love it' sort of way.

[kadoban]

You can indeed make the distinction between polynomial and pseudo-polynomial stop existing by enforcing the inputs are in unary. But you haven't made anything faster, you've just made almost all of them worse.