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Preprint Open Access

# The P versus NP Problem

Frank Vega

### Dublin Core Export

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<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:creator>Frank Vega</dc:creator>
<dc:date>2019-06-02</dc:date>
<dc:description>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.</dc:description>
<dc:identifier>https://zenodo.org/record/3239377</dc:identifier>
<dc:identifier>10.5281/zenodo.3239377</dc:identifier>
<dc:identifier>oai:zenodo.org:3239377</dc:identifier>
<dc:relation>doi:10.5281/zenodo.3237140</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:subject>Complexity Classes</dc:subject>
<dc:subject>Completeness</dc:subject>
<dc:subject>Polynomial Time</dc:subject>
<dc:subject>MONOTONE 1-IN-3 3SAT</dc:subject>
<dc:subject>2SET PACKING</dc:subject>
<dc:title>The P versus NP Problem</dc:title>
<dc:type>info:eu-repo/semantics/preprint</dc:type>
<dc:type>publication-preprint</dc:type>
</oai_dc:dc>

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