September 23, 2018 Preprint Open Access

Frank Vega

Citation Style Language JSON Export

{
  "publisher": "Zenodo", 
  "DOI": "10.5281/zenodo.1438785", 
  "author": [
    {
      "family": "Frank Vega"
    }
  ], 
  "issued": {
    "date-parts": [
      [
        2018, 
        9, 
        23
      ]
    ]
  }, 
  "abstract": "<pre>UP versus NP\n\nP 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.</pre>", 
  "title": "UP versus NP", 
  "type": "article", 
  "id": "1438785"
}