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atucker comments on Example decision theory problem: "Agent simulates predictor" - Less Wrong
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The N < M is necessary to guarantee that the agent predicts the predictor's proof, right?
What happens if the outlined proof is more than N symbols long?
Yeah. Actually, N must be exponentially smaller than M, so the agent's proofs can completely simulate the predictor's execution.
No idea. :-) Maybe the predictor will fail to prove anything, and fall back to filling only one box, I guess? Anyway, the outlined proof is quite short, so the problem already arises for not very large values of N.