Certainly P is a subset of NP, but is this statement always true?
Consider a Galton board where a marble is dropped into an array of pegs. At each peg, it can go left or right at random (assume it never bounces further). After some number of choices, it falls into a slot.
Finding a solution (a slot that a marble can fall into) is easy: drop one marble. But it could take many marbles to verify that a marble can fall into a given slot.
As described, that is easy: all left choices, all right choices, everything in between. But imagine that the choices aren't fair, directly observable, or linear (LR != RL). Then it gets tricky.
I've never thought about non-deterministic problems of that sort in the context of computational theory, but it isn't uncommon in nature.
