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Preprint Open Access

On P versus NP

Frank Vega


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  <identifier identifierType="DOI">10.5281/zenodo.2597704</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>On P versus NP</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2019</publicationYear>
  <subjects>
    <subject>P</subject>
    <subject>NP</subject>
    <subject>coNP</subject>
    <subject>coNP-complete</subject>
    <subject>Minimum</subject>
    <subject>Boolean circuit</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2019-03-19</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Preprint</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/2597704</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.2588891</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 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.&lt;/p&gt;</description>
    <description descriptionType="Other">Archived previous version in https://hal.archives-ouvertes.fr/hal-01509423</description>
  </descriptions>
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