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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>", 
  "license": "https://creativecommons.org/licenses/by/4.0/legalcode", 
  "creator": [
    {
      "affiliation": "Joysonic", 
      "@id": "https://orcid.org/0000-0001-8210-4126", 
      "@type": "Person", 
      "name": "Frank Vega"
    }
  ], 
  "headline": "Logarithmic Space Verifiers on NP-complete", 
  "image": "https://zenodo.org/static/img/logos/zenodo-gradient-round.svg", 
  "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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