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Preprint Open Access

On P versus NP

Frank Vega

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"description": "<p>P versus NP is considered as one of the great open problems of science. This consists in knowing the answer of the following question: Is P equal to NP? This problem was first mentioned in a letter written by John Nash to the National Security Agency in 1955. 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 huge problem have failed. Another major complexity class is coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. To attack the P versus NP problem, the concept of coNP-completeness is very useful. We prove there is a problem in coNP-complete that is not in P. In this way, we show that P is not equal to coNP. Since P = NP implies P = coNP, then we also demonstrate that P is not equal to NP.</p>",
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"title": "On P versus NP",
"notes": "Archived previous version in https://hal.archives-ouvertes.fr/hal-01509423",
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"P",
"NP",
"coNP",
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"Boolean circuit"
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