June 8, 2018 Preprint Open Access

Frank Vega

DCAT Export

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        <foaf:name>Frank Vega</foaf:name>
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    <dct:title>P vs NP</dct:title>
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    <dcat:keyword>Complexity Classes</dcat:keyword>
    <dcat:keyword>Completeness</dcat:keyword>
    <dcat:keyword>Polynomial Time</dcat:keyword>
    <dcat:keyword>3SAT</dcat:keyword>
    <dcat:keyword>Quadratic Residue</dcat:keyword>
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    <dct:description>&lt;p&gt;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 is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute. 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. To attack the P versus NP question the concept of NP-completeness has been very useful. If any single NP-complete problem can be solved in polynomial time, then every NP problem has a polynomial time algorithm. MONOTONE 3SAT is a known NP-complete problem. We prove MONOTONE 3SAT is in P. In this way, we demonstrate the P versus NP problem.&lt;/p&gt;</dct:description>
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