What is the implication of finding a proof that P NP?

3 Answers. If P=NP, then all of the NP problems can be solved deterministically in Polynomial time. This is because the NP problems are all essentially the same problem, just stated in different terms.

What are the implications if P NP?

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.

Can P NP be proven?

The statement P=NP means that if a problem takes polynomial time on a non-deterministic TM, then one can build a deterministic TM which would solve the same problem also in polynomial time. So far nobody has been able to show that it can be done, but nobody has been able to prove that it cannot be done, either.

Why is the P vs NP problem important in the field of computer science?

The P versus NP problem is a major unsolved problem in computer science. It asks whether every problem whose solution can be quickly verified can also be solved quickly. An answer to the P versus NP question would determine whether problems that can be verified in polynomial time can also be solved in polynomial time.

What does it mean for your NP-complete problem if P NP?

A problem p in NP is NP-complete if every other problem in NP can be transformed (or reduced) into p in polynomial time. It is not known whether every problem in NP can be quickly solved—this is called the P versus NP problem.

Is Othello NP complete?

Iwata and T. Kasai, The Othello game on an n*n board is PSPACE-complete, Theor.

Is there a proof for P=NP?

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 are the implications of P = NP in real life?

We will also have much better predictions of weather and earthquakes and other natural phenomenon. P = NP would also have big implications in mathematics. One could find short, fully logical proofs for theorems but these proofs are usually extremely long.

What are the consequences of a solution with Pn=NP?

P=NP will have lot of consequences : It will be possible to solve exactly optimization problems which are currently approximated. This is the case of the Travelling Salesman Problem and Job Scheduling Problem It breaks some security measures which are based on the fact that required computational time is enormous.

Does P = NP affect open problems in Computer Science?

Of course P = NP would affect a huge number of open problems in computer science, where certain problems are obviously in P, and obviously in NP but not known to be NP-complete, and it is unknown where exactly between P and NP they are – all these problems would be known to be in P.