A simple example of the exponential problem.
Given a bit string S of length N what is the probability to guess the value of the string ?
Given a set U of M bitstrings of length N and a string Su of U what is the probability to guess Su in U ?
Now if U is the set of all finite bitstrings available in an environment ( like the real world ) containing the problem and the solver what is the probability to find the solution for the problem ?
The key is that we are inside U and all the machines are inside U we can not construct bitstrings outside U ! and this is indipendently of deterministic or stochastic assumptions.