What happens if P is not equal to 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.

Is it possible for a problem to be in both P and NP True or false?

All problems in P can be solved with polynomial time algorithms, whereas all problems in NP – P are intractable. It is not known whether P = NP. However, many problems are known in NP with the property that if they belong to P, then it can be proved that P = NP.

Are all NP-Complete problems P equal to?

All -complete problems are equivalent in terms of “polynomial time solvability”, i.e. if one -complete problem has a polynomial time algorithm, then all of them belong to the class . This is true because any -complete problem reduces to any other -complete problem in polynomial time.

Can a problem be both P and NP-Complete?

The Boolean satisfiability problem is one of many such NP-complete problems. If any NP-complete problem is in P, then it would follow that P = NP. However, many important problems have been shown to be NP-complete, and no fast algorithm for any of them is known.

How P and NP problems are 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 every NP problem NP-complete?

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.

What’s the difference between P and NP?

P = the set of problems that are solvable in polynomial time by a Deterministic Turing Machine. NP = the set of decision problems (answer is either yes or no) that are solvable in nondeterministic polynomial time i.e can be solved in polynomial time by a Nondeterministic Turing Machine[4].

Is P equal to 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.

What is the difference between P = NP and NP -complete?

To attack the P = NP question, the concept of NP -completeness is very useful. NP -complete problems are a set of problems to each of which any other NP problem can be reduced in polynomial time and whose solution may still be verified in polynomial time. That is, any NP problem can be transformed into any of the NP -complete problems.

Is there a polynomial time algorithm for NP-complete problems?

No algorithm for any NP-complete problem is known to run in polynomial time. However, there are algorithms known for NP-complete problems with the property that if P = NP, then the algorithm runs in polynomial time on accepting instances (although with enormous constants, making the algorithm impractical).

Why do so many NP problems require exponential time?

Part of the question’s allure is that the vast majority of NP problems whose solutions seem to require exponential time are what’s called NP-complete, meaning that a polynomial-time solution to one can be adapted to solve all the others. And in real life, NP-complete problems are fairly common, especially in large scheduling tasks.

What is the history of the P versus NP problem?

The precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in his seminal paper “The complexity of theorem proving procedures” (and independently by Leonid Levin in 1973 ).