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For some questions, there is no known way to find an answer quickly, but if provided with an answer, it can be verified quickly. The class of questions where an answer can be verified in polynomial time is "NP", standing for "nondeterministic polynomial time". [Note 1] An answer to the P versus NP question would determine whether problems that ...
Since deterministic Turing machines are special non-deterministic Turing machines, it is easily observed that each problem in P is also member of the class NP. The question of whether P equals NP is one of the most important open questions in theoretical computer science because of the wide implications of a solution. [3]
"A large-scale quantum computer would be able to efficiently solve NP-complete problems." The class of decision problems that can be efficiently solved (in principle) by a fault-tolerant quantum computer is known as BQP. However, BQP is not believed to contain all of NP, and if it does not, then it cannot contain any NP-complete problem. [15]
The verifier-based definition of NP does not require an efficient verifier for the "no"-answers. The class of problems with such verifiers for the "no"-answers is called co-NP. In fact, it is an open question whether all problems in NP also have verifiers for the "no"-answers and thus are in co-NP.
The question is whether or not, for all problems for which an algorithm can verify a given solution quickly (that is, in polynomial time), an algorithm can also find that solution quickly. Since the former describes the class of problems termed NP, while the latter describes P, the question is equivalent to asking whether all problems in NP are ...
In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". [1] The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory.
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A vacuum-tube computer, now termed a first-generation computer, is a computer that uses vacuum tubes for logic circuitry. While the history of mechanical aids to computation goes back centuries , if not millennia , the history of vacuum tube computers is confined to the middle of the 20th century.