Can NP problems be solved how do u prove that problem is NP?

We can solve Y in polynomial time: reduce it to X. Therefore, every problem in NP has a polytime algorithm and P = NP. then X is NP-complete. In other words, we can prove a new problem is NP-complete by reducing some other NP-complete problem to it.

Can NP hard problems be verified in polynomial time?

An NP-Hard problem is one that is not solvable in polynomial time but can be verified in polynomial time.

Can be solved by a non-deterministic TM in polynomial time?

An equivalent definition of NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine. An algorithm solving such a problem in polynomial time is also able to solve any other NP problem in polynomial time.

How do you prove a problem is NP problem?

A problem is “in NP” if, given a potential solution, you can verify that it is correct or incorrect in polynomial time. For instance if the problem is sorting lists, if you can verify that one list is the sorted version of another list in polynomial time, then sorting is in NP.

How do you prove NP-hard problems?

To prove that problem A is NP-hard, reduce a known NP-hard problem to A. In other words, to prove that your problem is hard, you need to describe an ecient algorithm to solve a dierent problem, which you already know is hard, using an hypothetical ecient algorithm for your problem as a black-box subroutine.

Is NP non-deterministic?

What is Non-deterministic Polynomial Time? NP, for non-deterministic polynomial time, is one of the best-known complexity classes in theoretical computer science. A decision problem (a problem that has a yes/no answer) is said to be in NP if it is solvable in polynomial time by a non-deterministicTuring machine.

What happens when NP equals P?

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.