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Preprint Open Access

Logarithmic Space Verifiers on NP-complete

Frank Vega


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{
  "publisher": "Zenodo", 
  "DOI": "10.5281/zenodo.3355777", 
  "title": "Logarithmic Space Verifiers on NP-complete", 
  "issued": {
    "date-parts": [
      [
        2019, 
        7, 
        31
      ]
    ]
  }, 
  "abstract": "<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>", 
  "author": [
    {
      "family": "Frank Vega"
    }
  ], 
  "type": "article", 
  "id": "3355777"
}
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