September 23, 2018 Preprint Open Access

Frank Vega

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  <dc:creator>Frank Vega</dc:creator>
  <dc:date>2018-09-23</dc:date>
  <dc:description>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.</dc:description>
  <dc:identifier>https://zenodo.org/record/1438785</dc:identifier>
  <dc:identifier>10.5281/zenodo.1438785</dc:identifier>
  <dc:identifier>oai:zenodo.org:1438785</dc:identifier>
  <dc:relation>doi:10.5281/zenodo.1433418</dc:relation>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>https://creativecommons.org/licenses/by/4.0/legalcode</dc:rights>
  <dc:subject>Polynomial Time</dc:subject>
  <dc:subject>UP</dc:subject>
  <dc:subject>NP</dc:subject>
  <dc:subject>Quadratic Congruences</dc:subject>
  <dc:subject>NP-complete</dc:subject>
  <dc:title>UP versus NP</dc:title>
  <dc:type>info:eu-repo/semantics/preprint</dc:type>
  <dc:type>publication-preprint</dc:type>
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