[1arity]

> The original reduction was given by the well-known Cook-Levin theorem ...

That’s easy. The NTM is just a condensed representation of a DTM, and in each case, the machine encodes an algorithm for whatever NP problem you are working. “Guessing correctly” has no bearing on NP, and it’s not a scary or impossible property that it works for people to believe implies P == NP is false. “Guessing correctly” ( otherwise known as branching ) is simply a property of the NTM occupying more than one subsequent state. As long as you construct an algorithm such that the NTM branches on its guesses in P time ( or equivalently the DTM is P size), then you have the P time algorithm. Pretending a valid reason for P == NP being “widely believed to be false” because there would then exist “an NTM that supports guessing correctly as a primitive operation”, as if this should be somehow intuitively magical and impossible, is obfuscation, “guessing correctly” has nothing to do with NP and makes no problem harder or easier. “Guessing correctly” won’t make a shit algorithm good ( it’s not like an oracle in a quantum algorithm like Shor’s ), it’s just another way of describing a NTM. All you need to worry about is making that P time algorithm for some NP problem. Whether you want to implement that as a DTM or a NTM, is totally up to you. If it’s a P time algorithm it’s still a P time algorithm. I can make an EXP time algorithm in a NTM too if I like. “Guessing correctly” is not some magical speedup equivalent to P == NP. Too suggest that, or imply that, by suggesting that such a machine would somehow be magical is either the result of someone who doesn’t understand this, or someone who is choosing to obfuscate this. So either you don’t understand it, and you are pretending that you do. Or you do understand it and you are needlessly fabricating to try to argue for P !== NP, simply revealing how tenuous you fear the arguments are, and how deeply you lack any substantive ones that you must fabricate them. Your language is an attempt to obfuscate and incorrectly attempt to confuse people who don’t understand. If you really know this space, doing that is just balderdash. Well played.