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# The P versus NP Problem

Frank Vega

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{
"description": "<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>",
"license": "http://creativecommons.org/licenses/by/4.0/legalcode",
"creator": [
{
"affiliation": "Joysonic",
"@id": "https://orcid.org/0000-0001-8210-4126",
"@type": "Person",
"name": "Frank Vega"
}
],
"headline": "The P versus NP Problem",
"image": "https://zenodo.org/static/img/logos/zenodo-gradient-round.svg",
"datePublished": "2019-06-02",
"url": "https://zenodo.org/record/3239377",
"keywords": [
"Complexity Classes",
"Completeness",
"Polynomial Time",
"MONOTONE 1-IN-3 3SAT",
"2SET PACKING"
],
"@context": "https://schema.org/",
"identifier": "https://doi.org/10.5281/zenodo.3239377",
"@id": "https://doi.org/10.5281/zenodo.3239377",
"@type": "ScholarlyArticle",
"name": "The P versus NP Problem"
}
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