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Published June 27, 2020 | Version v67
Preprint Open

P versus NP

Creators

  • 1. Joysonic

Description

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. Another major complexity class is Sharp-P-complete. A polynomial time algorithm for solving a Sharp-P-complete problem, if it existed, then this would solve the P versus NP problem by implying that P and NP are equal. We demonstrate there is a problem in Sharp-P-complete that can be solved in polynomial time. In this way, we prove the complexity class P is equal to NP.

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