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What happens if P NP is solved?
If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them. But if P does not equal NP, then no such shortcuts exist, and computers’ problem-solving powers will remain fundamentally and permanently limited.
What would you gain if P NP?
But, if P = NP, then MAS and SUBSET–PRODUCT would be in P–complete, because they are NP–complete. This proof explains why after decades of studying the NP problems no one has been able to find a polynomial-time algorithm for any of more than 300 important known NP–complete problems [4].
Is Bitcoin mining an NP?
No. Bitcoin mining can be solved in O(1) time. Unfortunately the hidden constant is quite large.
Are P problems NP problems?
Roughly speaking, P is a set of relatively easy problems, and NP is a set that includes what seem to be very, very hard problems, so P = NP would imply that the apparently hard problems actually have relatively easy solutions.
How does a proof for P = NP work?
A proof would involve finding a polynomial time algorithm for an NP-complete problem. And when you find one polynomial algorithm, you can use it to solve all other NP-complete problems by reducing the problems to a common form. This means that a proof for P=NP and algorithms that use it will appear at the same time.
What happens to PKC if P = NP?
If P = NP, everything that depends on PKC (including HTTPS, which means the entire modern, worldwide ecommerce infrastructure) would have to be reworked! This is covered in The Status of the P Versus NP Problem. Definitely worth a read. A few salient points from the article (quoted from the What If P = NP? section ):
Are there any problems known to be NP complete?
The bottom line is on the nature of the problems known to be NP-complete. These are not just problems created by few scientists in a remote location to entertain each other. They can be expressed in business terms. In fact, some job interviewers like to conceal NP-complete problems in their questions in order to test candidates.
What’s the difference between a p and a NP?
Roughly speaking, P is a set of relatively easy problems, and NP is a set that includes what seem to be very, very hard problems, so P = NP would imply that the apparently hard problems actually have relatively easy solutions.