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by JadeNB
3509 days ago
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> Yes, since we could just not invoke the oracle. I think that only shows that P^X contains P and NP^X contains NP, not that P = NP implies P^X = NP^X. Indeed, my supposition that this implication holds seems to be false; openasocket (https://news.ycombinator.com/item?id=12893077) points to a paper mentioning a specific example of an oracle B so that P^B \ne NP^B. If my naïve reasoning were correct, then we'd be able to deduce that P \ne NP; but we famously can't. |
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