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## P versus NP Answer

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posted on 17.04.2018 by Frank Vega#### online resource

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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? This question was first mentioned in a letter written by John Nash to the National Security Agency in 1955. A precise statement of the P versus NP problem was introduced independently in 1971 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. OTHER-L is a problem of deciding given a solution y of an instance x in a language L whether x has another solution different of y. The class OTHER-NP contains those languages OTHER-L where L is in NP. Another major complexity class is NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. We show a previous known OTHER-NP language which is NP-complete. If any single NP-complete problem can be solved in polynomial time, then every NP problem has a polynomial time algorithm. Therefore, if P = OTHER-NP, then P = NP. Moreover, we show OTHER-SAT and OTHER-3SAT are complete for OTHER-NP. Furthermore, we show OTHER-SAT is NP-complete as well. Indeed, we prove OTHER-3SAT is not only complete for OTHER-NP, but it is also in P. In this way, we demonstrate the P versus NP problem.