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Preprint Open Access

UP versus NP

Frank Vega


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  <identifier identifierType="DOI">10.5281/zenodo.1433419</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>UP versus NP</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2018</publicationYear>
  <subjects>
    <subject>Polynomial Time</subject>
    <subject>UP</subject>
    <subject>NP</subject>
    <subject>Quadratic Congruences</subject>
    <subject>NP-complete</subject>
  </subjects>
  <dates>
    <date dateType="Issued">2018-09-23</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Preprint</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/1433419</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.1433418</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="https://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;pre&gt;UP versus NP

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 in 1971 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 UP. Whether UP = NP is another fundamental question that it is as important as it is unresolved. To attack the UP = NP question the concept of NP-completeness is very useful. If any single NP-complete problem is in UP, then UP = NP. Quadratic Congruences is a well-known NP-complete problem. We prove Quadratic Congruences is also in UP. In this way, we demonstrate that UP = NP.&lt;/pre&gt;</description>
  </descriptions>
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