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Preprint Open Access

Logarithmic Space Verifiers on NP-complete

Frank Vega

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<foaf:name>Frank Vega</foaf:name>
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<dct:title>Logarithmic Space Verifiers on NP-complete</dct:title>
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<dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#gYear">2019</dct:issued>
<dcat:keyword>Complexity classes</dcat:keyword>
<dcat:keyword>Completeness</dcat:keyword>
<dcat:keyword>Verifier</dcat:keyword>
<dcat:keyword>Reduction</dcat:keyword>
<dcat:keyword>Polynomial time</dcat:keyword>
<dcat:keyword>Logarithmic space</dcat:keyword>
<dct:issued rdf:datatype="http://www.w3.org/2001/XMLSchema#date">2019-07-31</dct:issued>
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<dct:description>&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. 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.&lt;/p&gt;</dct:description>
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