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Preprint Open Access

The P versus NP Problem

Frank Vega


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    <dct:title>The P versus NP Problem</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>MONOTONE 1-IN-3 3SAT</dcat:keyword>
    <dcat:keyword>2SET PACKING</dcat:keyword>
    <dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-06-02</dct:issued>
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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? 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. To attack the P versus NP problem, the NP-completeness is a useful tool. We prove the known NP-complete problem MONOTONE 1-IN-3 3SAT can be polynomially reduced to the polynomial language 2SET PACKING. In this way, MONOTONE 1-IN-3 3SAT must be in P. If any NP-complete problem can be solved in polynomial time, then every language in NP has a polynomial time algorithm. Hence, we demonstrate the complexity class P is equal to NP.&lt;/p&gt;</dct:description>
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