Incoming links: NP-complete
Term invented by Ciro Santilli to refer to problems that can only be solved once we have AGI.
It is somewhat of a flawed analogy to NP-complete.
P for quantum computing!
Heck, we know nothing about this class yet related to non quantum classes!
- conjectured not to intersect with NP-complete, because if it were, all NP-complete problems could be solved efficiently on quantum computers, and none has been found so far as of 2020.
- conjectured to be larger than P, but we don't have a single algorithm provenly there:
- it is believed that the NP complete ones can't be solved
- if they were neither NP-complete nor P, it would imply P != NP
- we just don't know if it is even contained inside NP!
Complexity: NP-intermediate as of 2020:
- expected not to be NP-complete because it would imply NP != Co-NP: cstheory.stackexchange.com/questions/167/what-are-the-consequences-of-factoring-being-np-complete#comment104849_169
- expected not to be in P because "could we be that dumb that we haven't found a solution after having tried for that long?
The basis of RSA: RSA. But not proved NP-complete, which leads to:
This is the most interesting class of problems for BQP as we haven't proven that they are neither:
- P: would be boring on quantum computer
- NP-complete: would likely be impossible on a quantum computer
Interesting because of the Cook-Levin theorem: if only a single NP-complete problem were in P, then all NP-complete problems would also be P!
We all know the answer for this: either false or independent.