Preprint Open Access

# On P versus NP

Frank Vega

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<dc:creator>Frank Vega</dc:creator>
<dc:date>2019-03-19</dc:date>
<dc:description>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 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. We prove there is a problem in coNP 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.</dc:description>
<dc:description>Archived previous version in https://hal.archives-ouvertes.fr/hal-01509423</dc:description>
<dc:identifier>https://zenodo.org/record/2598772</dc:identifier>
<dc:identifier>10.5281/zenodo.2598772</dc:identifier>
<dc:identifier>oai:zenodo.org:2598772</dc:identifier>
<dc:relation>doi:10.5281/zenodo.2588891</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:subject>P</dc:subject>
<dc:subject>NP</dc:subject>
<dc:subject>coNP</dc:subject>
<dc:subject>coNP-complete</dc:subject>
<dc:subject>Minimum</dc:subject>
<dc:subject>Boolean circuit</dc:subject>
<dc:title>On P versus NP</dc:title>
<dc:type>info:eu-repo/semantics/preprint</dc:type>
<dc:type>publication-preprint</dc:type>
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