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Preprint Open Access

# The P versus NP Problem

Frank Vega

### DataCite XML Export

<?xml version='1.0' encoding='utf-8'?>
<identifier identifierType="DOI">10.5281/zenodo.3239377</identifier>
<creators>
<creator>
<creatorName>Frank Vega</creatorName>
<nameIdentifier nameIdentifierScheme="ORCID" schemeURI="http://orcid.org/">0000-0001-8210-4126</nameIdentifier>
<affiliation>Joysonic</affiliation>
</creator>
</creators>
<titles>
<title>The P versus NP Problem</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2019</publicationYear>
<subjects>
<subject>Complexity Classes</subject>
<subject>Completeness</subject>
<subject>Polynomial Time</subject>
<subject>MONOTONE 1-IN-3 3SAT</subject>
<subject>2SET PACKING</subject>
</subjects>
<dates>
<date dateType="Issued">2019-06-02</date>
</dates>
<resourceType resourceTypeGeneral="Text">Preprint</resourceType>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/3239377</alternateIdentifier>
</alternateIdentifiers>
<relatedIdentifiers>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.3237140</relatedIdentifier>
</relatedIdentifiers>
<rightsList>
<rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
</rightsList>
<descriptions>
<description descriptionType="Abstract">&lt;p&gt;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.&lt;/p&gt;</description>
</descriptions>
</resource>

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