Preprint Open Access
<?xml version='1.0' encoding='UTF-8'?> <record xmlns="http://www.loc.gov/MARC21/slim"> <leader>00000nam##2200000uu#4500</leader> <datafield tag="653" ind1=" " ind2=" "> <subfield code="a">Polynomial Time</subfield> </datafield> <datafield tag="653" ind1=" " ind2=" "> <subfield code="a">UP</subfield> </datafield> <datafield tag="653" ind1=" " ind2=" "> <subfield code="a">NP</subfield> </datafield> <datafield tag="653" ind1=" " ind2=" "> <subfield code="a">Quadratic Congruences</subfield> </datafield> <datafield tag="653" ind1=" " ind2=" "> <subfield code="a">NP-complete</subfield> </datafield> <controlfield tag="005">20200120174555.0</controlfield> <controlfield tag="001">1438821</controlfield> <datafield tag="856" ind1="4" ind2=" "> <subfield code="s">237467</subfield> <subfield code="z">md5:eccc3cb3a446afd1d3749216e0ba7844</subfield> <subfield code="u">https://zenodo.org/record/1438821/files/manuscript.pdf</subfield> </datafield> <datafield tag="542" ind1=" " ind2=" "> <subfield code="l">open</subfield> </datafield> <datafield tag="260" ind1=" " ind2=" "> <subfield code="c">2018-09-23</subfield> </datafield> <datafield tag="909" ind1="C" ind2="O"> <subfield code="p">openaire</subfield> <subfield code="o">oai:zenodo.org:1438821</subfield> </datafield> <datafield tag="100" ind1=" " ind2=" "> <subfield code="u">Joysonic</subfield> <subfield code="0">(orcid)0000-0001-8210-4126</subfield> <subfield code="a">Frank Vega</subfield> </datafield> <datafield tag="245" ind1=" " ind2=" "> <subfield code="a">UP versus NP</subfield> </datafield> <datafield tag="540" ind1=" " ind2=" "> <subfield code="u">https://creativecommons.org/licenses/by/4.0/legalcode</subfield> <subfield code="a">Creative Commons Attribution 4.0 International</subfield> </datafield> <datafield tag="650" ind1="1" ind2="7"> <subfield code="a">cc-by</subfield> <subfield code="2">opendefinition.org</subfield> </datafield> <datafield tag="520" ind1=" " ind2=" "> <subfield code="a"><pre>UP versus NP 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 UP. Whether UP = NP is another fundamental question that it is as important as it is unresolved. To attack the UP = NP question the concept of NP-completeness is very useful. If any single NP-complete problem is in UP, then UP = NP. Quadratic Congruences is a well-known NP-complete problem. We prove Quadratic Congruences is also in UP. In this way, we demonstrate that UP = NP.</pre></subfield> </datafield> <datafield tag="773" ind1=" " ind2=" "> <subfield code="n">doi</subfield> <subfield code="i">isVersionOf</subfield> <subfield code="a">10.5281/zenodo.1433418</subfield> </datafield> <datafield tag="024" ind1=" " ind2=" "> <subfield code="a">10.5281/zenodo.1438821</subfield> <subfield code="2">doi</subfield> </datafield> <datafield tag="980" ind1=" " ind2=" "> <subfield code="a">publication</subfield> <subfield code="b">preprint</subfield> </datafield> </record>
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