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NP-complete problems can be polynomially reduced to each other. If you had a magical oracle that was able to solve any one specific NP-complete problem in O(1)
by qsort 6y ago
NP-complete problems can be polynomially reduced to each other. If you had a magical oracle that was able to solve any one specific NP-complete problem in O(1) time, you could turn that into a O(n^k) solution for all NP-complete problems.
That's the idea behind DNA-computing, for instance.
The question is whether it is actually possible to do so at a reasonable cost and at scale.
Regardless, what "nature" does has 0 to do with P vs NP, computability or anything else. P vs NP is a statement strictly about mathematical objects, there is no notion of "nature" anywhere in it.