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Pré-Publication, Document De Travail Année : 2019

Logarithmic Space Verifiers on NP-complete

Frank Vega

Résumé

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.
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Dates et versions

hal-02199310 , version 1 (31-07-2019)
hal-02199310 , version 2 (01-08-2019)
hal-02199310 , version 3 (08-08-2019)
hal-02199310 , version 4 (12-08-2019)
hal-02199310 , version 5 (20-09-2019)
hal-02199310 , version 6 (13-10-2019)
hal-02199310 , version 7 (03-11-2019)
hal-02199310 , version 8 (10-02-2020)
hal-02199310 , version 9 (16-04-2020)
hal-02199310 , version 10 (26-04-2020)
hal-02199310 , version 11 (19-07-2020)
hal-02199310 , version 12 (18-09-2020)
hal-02199310 , version 13 (06-10-2020)
hal-02199310 , version 14 (28-12-2020)

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  • HAL Id : hal-02199310 , version 1

Citer

Frank Vega. Logarithmic Space Verifiers on NP-complete. 2019. ⟨hal-02199310v1⟩
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