![]() ![]() ![]() This definition is the basis for the abbreviation NP " nondeterministic, polynomial time." These two definitions are equivalent because the algorithm based on the Turing machine consists of two phases, the first of which consists of a guess about the solution, which is generated in a nondeterministic way, while the second phase consists of a deterministic algorithm that verifies if the guess is a solution to the problem. Īn equivalent definition of NP is the set of decision problems solvable in polynomial time by a nondeterministic Turing machine. NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. In computational complexity theory, NP ( nondeterministic polynomial time) is a complexity class used to classify decision problems. Under the assumption that P≠NP, the existence of problems within NP but outside both P and NP-complete was established by Ladner. Euler diagram for P, NP, NP-complete, and NP-hard set of problems.
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