Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

P versus NP

Version 1 : Received: 1 August 2019 / Approved: 5 August 2019 / Online: 5 August 2019 (03:31:23 CEST)
Version 2 : Received: 26 November 2019 / Approved: 29 November 2019 / Online: 29 November 2019 (07:28:14 CET)
Version 3 : Received: 4 April 2020 / Approved: 6 April 2020 / Online: 6 April 2020 (12:57:55 CEST)
Version 4 : Received: 15 April 2020 / Approved: 16 April 2020 / Online: 16 April 2020 (10:17:03 CEST)
Version 5 : Received: 18 September 2020 / Approved: 19 September 2020 / Online: 19 September 2020 (09:51:02 CEST)

How to cite: Vega, F. P versus NP. Preprints 2019, 2019080037 (doi: 10.20944/preprints201908.0037.v2). Vega, F. P versus NP. Preprints 2019, 2019080037 (doi: 10.20944/preprints201908.0037.v2).


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? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, 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. Another major complexity classes are L and NL. Whether L = NL is another fundamental question that it is as important as it is unresolved. We demonstrate that every problem in NP could be NL-reduced to another problem in L.

Subject Areas

complexity classes; completeness; polynomial time; reduction; logarithmic space; one-way

Comments (1)

Comment 1
Received: 29 November 2019
Commenter: Frank Vega
Commenter's Conflict of Interests: Author
Comment: The document was changed. The title, abstract and keywords change as well. In this way, it is necessary to update the html page of the preprint site.
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