What if P is not 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.
Are NP problems Turing computable?
Since NP problems are computable, every NP problem is polynomial-time reducible to H, so H is NP-hard. The other important way to build a non-computable, NP-hard problem is to observe that we can combine any known NP-hard problem with any known non-computable problem.
Are there problems in NP that are not NP-complete?
There are many decision problems that are NP-hard but not NP-complete. A simple example is the Halting problem for Turing machines. Any problem in NP can easily be reduced to the Halting problem.
Is it true that if an NP-complete problem can be solved in polynomial time then P NP justify your answer?
The answer is B (no NP-Complete problem can be solved in polynomial time). Because, if one NP-Complete problem can be solved in polynomial time, then all NP problems can solved in polynomial time. If that is the case, then NP and P set become same which contradicts the given condition.
Why P NP is important?
Now, if P=NP, we could find solutions to search problems as easily as checking whether those solutions are good. This would essentially solve all the algorithmic challenges that we face today and computers could solve almost any task.
What is the difference between P and 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.
What is NP algorithm?
NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found.
Is P contained in NP?
It is easy to see that the complexity class P (all problems solvable, deterministically, in polynomial time) is contained in NP (problems where solutions can be verified in polynomial time), because if a problem is solvable in polynomial time then a solution is also verifiable in polynomial time by simply solving the …
Are all P problems 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.
Which problem is not NP-complete?
Which of the following problems is not NP complete? Explanation: Hamiltonian circuit, bin packing, partition problems are NP complete problems. Halting problem is an undecidable problem.
Has P versus NP been solved?
Although one-way functions have never been formally proven to exist, most mathematicians believe that they do, and a proof of their existence would be a much stronger statement than P ≠ NP. Thus it is unlikely that natural proofs alone can resolve P = NP.
Does P NP mean?
P is the set of problems whose solution times are proportional to polynomials involving N’s. NP (which stands for nondeterministic polynomial time) is the set of problems whose solutions can be verified in polynomial time. But as far as anyone can tell, many of those problems take exponential time to solve.