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# Logarithmic Space Verifiers on NP-complete

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>2019-07-31</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. NP is the complexity class of languages defined by polynomial time verifiers M such that when the input is an element of the language with its certificate, then M outputs a string which belongs to a single language in P. Another major complexity classes are L and NL. The certificate-based definition of NL is based on logarithmic space Turing machine with an additional special read-once input tape: This is called a logarithmic space verifier. NL is the complexity class of languages defined by logarithmic space verifiers M such that when the input is an element of the language with its certificate, then M outputs 1. To attack the P versus NP problem, the NP-completeness is a useful concept. We demonstrate there is an NP-complete language defined by a logarithmic space verifier M such that when the input is an element of the language with its certificate, then M outputs a string which belongs to a single language in L.</dc:description>
<dc:identifier>https://zenodo.org/record/3355777</dc:identifier>
<dc:identifier>10.5281/zenodo.3355777</dc:identifier>
<dc:identifier>oai:zenodo.org:3355777</dc:identifier>
<dc:relation>doi:10.5281/zenodo.3355776</dc:relation>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:subject>Complexity classes</dc:subject>
<dc:subject>Completeness</dc:subject>
<dc:subject>Verifier</dc:subject>
<dc:subject>Reduction</dc:subject>
<dc:subject>Polynomial time</dc:subject>
<dc:subject>Logarithmic space</dc:subject>
<dc:title>Logarithmic Space Verifiers on NP-complete</dc:title>
<dc:type>info:eu-repo/semantics/preprint</dc:type>
<dc:type>publication-preprint</dc:type>
</oai_dc:dc>

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