It gives that as an upper bound on the size of the search space of boolean functions with n-bit input, representing technical strategies that consider the last n market movements. It goes on to claim that if there is a historically winning technical strategy, a nondeterministic Turing machine can write out a full description of that strategy in polynomial time.
The remaining problem is how to uniquely describe in polynomial space an element of a set with doubly exponentially many elements, but the authors don't bring that up because they're working under the assumption that there are 2^n functions rather than 2^(2^n).
The assertion that the efficient market hypothesis is equivalent to P=NP also comes with no proof that future performance of a trading strategy will match its past performance or that anyone will actually deploy a perfect strategy if one exists.
The remaining problem is how to uniquely describe in polynomial space an element of a set with doubly exponentially many elements, but the authors don't bring that up because they're working under the assumption that there are 2^n functions rather than 2^(2^n).
The assertion that the efficient market hypothesis is equivalent to P=NP also comes with no proof that future performance of a trading strategy will match its past performance or that anyone will actually deploy a perfect strategy if one exists.