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P versus NP

Frank Vega

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. Another major complexity classes are L and NL. Whether L = NL is another fundamental question that it is as important as it is unresolved. We demonstrate if L is not equal to NL, then P = NP. In addition, we show if L is equal to NL, then P = NP. In this way, we prove the complexity class P is equal to NP. Furthermore, we demonstrate the complexity class NL is equal to NP.

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