[adamnemecek]

> unless you are saying that in an analog case we can ignore the rules of the maze and can go through walls.

Not ignore, but you have a lot more information about the problem and you have a general direction of the solution.

ND turing can split and like explore multiple corridors at once. But in the end all those robots that don't end up finding exit just wasted energy. I guess you don't care about this in complexity theory but this is a huge gain in practice.

[techdragon]

The description makes me think of a loud sound echoing through the maze, each branch further divides the volume of the sound, but a loud enough sound will "exit" in the optimal "O(1)" time because the sound wave "explores" every branch of the maze in "parallel".

Is this a reasonable mental model of what your describing?

[adamnemecek]

In your description you are still expending extra energy to explore the branches. Also it's not O(1), it's just that every step you take is bound to be optimal. So in O(1), you are literally one step closer to the solution.