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Preprint Open Access

The P versus NP Problem

Frank Vega


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{
  "publisher": "Zenodo", 
  "DOI": "10.5281/zenodo.3239377", 
  "title": "The P versus NP Problem", 
  "issued": {
    "date-parts": [
      [
        2019, 
        6, 
        2
      ]
    ]
  }, 
  "abstract": "<p>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 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. To attack the P versus NP problem, the NP-completeness is a useful tool. We prove the known NP-complete problem MONOTONE 1-IN-3 3SAT can be polynomially reduced to the polynomial language 2SET PACKING. In this way, MONOTONE 1-IN-3 3SAT must be in P. If any NP-complete problem can be solved in polynomial time, then every language in NP has a polynomial time algorithm. Hence, we demonstrate the complexity class P is equal to NP.</p>", 
  "author": [
    {
      "family": "Frank Vega"
    }
  ], 
  "type": "article", 
  "id": "3239377"
}
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