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UP versus NP

Frank Vega

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  "publisher": "Zenodo", 
  "DOI": "10.5281/zenodo.1438821", 
  "author": [
      "family": "Frank Vega"
  "issued": {
    "date-parts": [
  "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": "1438821"
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