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# Sparse complete sets for coNP: Solution of the P versus NP problem

Frank Vega

### DataCite XML Export

<?xml version='1.0' encoding='utf-8'?>
<identifier identifierType="DOI">10.5281/zenodo.1420486</identifier>
<creators>
<creator>
<creatorName>Frank Vega</creatorName>
<affiliation>Joysonic</affiliation>
</creator>
</creators>
<titles>
<title>Sparse complete sets for coNP: Solution of the P versus NP problem</title>
</titles>
<publisher>Zenodo</publisher>
<publicationYear>2018</publicationYear>
<subjects>
<subject>Complexity Classes</subject>
<subject>Sparse</subject>
<subject>Complement Language</subject>
<subject>Completeness</subject>
<subject>Polynomial Time</subject>
</subjects>
<dates>
<date dateType="Issued">2018-09-17</date>
</dates>
<resourceType resourceTypeGeneral="Text">Preprint</resourceType>
<alternateIdentifiers>
<alternateIdentifier alternateIdentifierType="url">https://zenodo.org/record/1420486</alternateIdentifier>
</alternateIdentifiers>
<relatedIdentifiers>
<relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.5281/zenodo.1420485</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 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 coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. In 1979, Fortune showed that if any sparse language is coNP-complete, then P = NP. We prove there is a possible sparse language in coNP-complete. In this way, we demonstrate the complexity class P is equal to NP.&lt;/p&gt;</description>
</descriptions>
</resource>

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