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P versus NP problem

The relationship between the [complexity class] ** es ** [P] ** and ** [NP] is an unsolved question in [theoretical computer science] and is also considered to be one of the most important open questions in [mathematics] . It is considered by many theoretical computer scientists to be the most important problem in the field. [Lance Fortnow] , [''The status of the P versus NP problem''] , Communications of the ACM 52 (2009), no. 9, pp. 78–86. The [Clay Mathematics Institute] , which is dedicated to increasing and disseminating mathematical knowledge, has offered a million dollar [prize] for solving this question.

In essence, the question ** P ** = ** NP ** ? asks: if 'yes'-answers to a ['yes'-or-'no'-question] can be * verified * "quickly" (in [polynomial time] ) can the answers themselves also be * computed * quickly?

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