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Nisan comments on AI cooperation in practice - Less Wrong
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Only a very rough one, I'm afraid. The number n1 is chosen to "contain" the blow-up from the short proof of 10 to the proof of 11, which grows with the computational complexities of n1,...,nmax, not their values. These computational complexities can be made way smaller than n1.
Why is this true? I am trying to understand. An obvious way to prove that eval(box) returns true is to go through the execution step by step. But when I write down what box is, it seems to call proves(box, n1) and eval(outputs(1)), which take much more than n1 steps.
n1 is chosen as to contain the size of the "box" statement, not its execution time.