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Can you explain the P versus NP problem to me?

Can you explain the P versus NP problem to me?

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 is the difference between P and NP class?

Step 1 − If a problem is in class P, it is nothing but we can find a solution to that type of problem in polynomial time. Step 2 − If a problem is in class NP, it is nothing but that we can verify a possible solution in polynomial time.

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What is the difference between P and NP class problems?

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].

Why is P versus NP important?

But “P versus NP” is more than just an abstract mathematical puzzle. It seeks to determine–once and for all–which kinds of problems can be solved by computers, and which kinds cannot. If P equals NP, every NP problem would contain a hidden shortcut, allowing computers to quickly find perfect solutions to them.

What is the meaning of P NP?

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.

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What is the relationship between the classes P and NP explain?

NP is set of problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. P is subset of NP (any problem that can be solved by deterministic machine in polynomial time can also be solved by non-deterministic machine in polynomial time) but 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.

What is the difference between P and NP complete?

P is the class of decision problems which can be solved in polynomial time by a deterministic Turing machine. NP is the class of decision problems which can be solved in polynomial time by a non-deterministic Turing machine.

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What is P and NP example?

Thus if any one NP-Complete problem can be solved in polynomial time, then every NP-Complete problem can be solved in polynomial time, and every problem in NP can be solved in polynomial time (i.e. P=NP). The most famous example would be the Traveling Salesmen problem.