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Preprint Open Access

The P versus NP Problem

Frank Vega


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  <identifier identifierType="DOI">10.5281/zenodo.3239377</identifier>
  <creators>
    <creator>
      <creatorName>Frank Vega</creatorName>
      <nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0001-8210-4126</nameIdentifier>
      <affiliation>Joysonic</affiliation>
    </creator>
  </creators>
  <titles>
    <title>The P versus NP Problem</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2019</publicationYear>
  <subjects>
    <subject>Complexity Classes</subject>
    <subject>Completeness</subject>
    <subject>Polynomial Time</subject>
    <subject>MONOTONE 1-IN-3 3SAT</subject>
    <subject>2SET PACKING</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2019-06-02</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Preprint</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/3239377</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.3237140</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://creativecommons.org/licenses/by/4.0/legalcode">Creative Commons Attribution 4.0 International</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&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;</description>
  </descriptions>
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