What is the solution of P vs 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. But the details are more complicated.

How are P and NP problems related?

P is set of problems that can be solved by a deterministic Turing machine in Polynomial time. NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time.

Is there a solution to the P vs NP problem?

While the P versus NP problem is generally considered unsolved, many amateur and some professional researchers have claimed solutions. Gerhard J. Woeginger maintains a list that, as of 2018, contains 62 purported proofs of P = NP, 50 of P ≠ NP, 2 proofs the problem is unprovable, and one proof that it is undecidable.

What is the history of NP-complete problems?

Steve Cook, Leonid Levin, and Richard Karp 10, 24, 27 developed the initial theory of NP -completeness that generated multiple ACM Turing Awards. In the 1970s, theoretical computer scientists showed hundreds more problems NP -complete (see Garey and Johnson 16 ).

What are some real-world applications of P = NP?

An example of a field that could be uprooted by a solution showing P = NP is cryptography, which relies on certain problems being difficult. A constructive and efficient solution to an NP -complete problem such as 3-SAT would break most existing cryptosystems including:

What does P = NP mean in math?

The collection of problems that have efficiently verifiable solutions is known as NP (for “Nondeterministic Polynomial-Time,” if you have to ask). So P = NP means that for every problem that has an efficiently verifiable solution, we can find that solution efficiently as well.