The Halting Problem is a terrible example of NP-Harder

The example given doesn't seem right to me.

> There is one problem, though, that I find easily explainable. Place a token at the bottom left corner of a grid that extends infinitely up and right, call that point (0, 0). You're given list of valid displacement moves for the token, like (+1, +0), (-20, +13), (-5, -6), etc, and a target point like (700, 1). You may make any sequence of moves in any order, as long as no move ever puts the token off the grid. Does any sequence of moves bring you to the target?

If someone gives you such a sequence, it seems trivial to verify it in linear time. Even for arbitrary dimensions, and such witness can be verified in linear time.

Linear time in the length of the sequence, yes. But is the sequence length linear in dimension size, or number of moves given? Thats what is interesting.

It doesn’t need to be linear though. Polynomial is enough.

But I guess it can be proven that the shortest possible sequence grows faster than polynomial.

I think they proved it grows with Ackermann function.

Sounds implausible… Number of computational steps to find the shortest sequence maybe grows with Ackermann function. But length of the shortest sequence?