Can NP be solved in polynomial time?

Can NP be solved in polynomial time?

If an NP-complete problem can be solved in polynomial time then all problems in NP can be solved in polynomial time. If a problem in NP cannot be solved in polynomial time then all problems in NP-complete cannot be solved in polynomial time. Note that an NP-complete problem is one of those hardest problems in NP.

Can quantum computers solve NP problems in polynomial time?

Quantum computers can solve NP-hard problems that classical computers are unable to solve. Currently, the two most important and notable complexity classes are “P” and “NP.” P represents problems that can be solved in polynomial time by a classical computer. For instance, asking if a number is prime belongs to P.

Are NP-hard problems verifiable in polynomial time?

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

Which algorithm takes polynomial time for completion of problem?

What are NP, P, NP-complete and NP-Hard problems? P is set of problems that can be solved by a deterministic Turing machine in Polynomial time. NP is set of decision problems that can be solved by a Non-deterministic Turing Machine in Polynomial time.

Can NP-complete problems be solved?

The NP-complete problems represent the hardest problems in NP. If some NP-complete problem has a polynomial time algorithm, all problems in NP do. Although a solution to an NP-complete problem can be verified “quickly”, there is no known way to find a solution quickly.

Which is the example of polynomial algorithm?

Problems that can be solved by a polynomial-time algorithm are called tractable problems. For example, most algorithms on arrays can use the array size, n, as the input size. To find the largest element in an array requires a single pass through the array, so the algorithm for doing this is O(n), or linear time.

Can a NP complete problem be solved in polynomial time?

Based on the below link , I can know that solving of Satisfiability (NP Complete) in polynomial time means any other NP problem can be solved in polynomial time. But is Vice – Versa true? Also, If there is a polynimial for any other NP-Complete problemt does it mean , all the other NP-Complete can be solved in polynomial time?

Can a non deterministic Turing machine solve a polynomial time problem?

Solved in polynomial time by a non deterministic turing machine. (there exists non deterministic Turing Machine M that can solve the problem polynomially) Since by definition of NP-Complete – a problem is NP Complete if it is NP-Hard AND in NP, every NP-Complete problem is also NP – and both are correct.

What does it mean when a problem is NP complete?

The ‘complete’ in NP-complete means that if a problem is in NP-complete, a solution for that problem gives a solution to any problem in NP with a polynomial amount of conversion processing. In layman’s terms – if you solve a single NP-complete problem in polynomial time you have proven that NP = P.

Which is the class of non deterministic polynomial problems?

• Class NP (Non-deterministic Polynomial) is the class of decision problems that can be solved by non-deterministic polynomial algorithms. • Note that all problems in Class P are in Class NP: We can replace the non-deterministic guessing of Stage 1 with the deterministic algorithm for the decision problem, and then in Stage 2,