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# Logarithmic Space Verifiers on NP-complete

Frank Vega

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{
"description": "<p>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.</p>",
"creator": [
{
"affiliation": "Joysonic",
"@id": "https://orcid.org/0000-0001-8210-4126",
"@type": "Person",
"name": "Frank Vega"
}
],
"headline": "Logarithmic Space Verifiers on NP-complete",
"datePublished": "2019-07-31",
"url": "https://zenodo.org/record/3355777",
"keywords": [
"Complexity classes",
"Completeness",
"Verifier",
"Reduction",
"Polynomial time",
"Logarithmic space"
],
"@context": "https://schema.org/",
"identifier": "https://doi.org/10.5281/zenodo.3355777",
"@id": "https://doi.org/10.5281/zenodo.3355777",
"@type": "ScholarlyArticle",
"name": "Logarithmic Space Verifiers on NP-complete"
}
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