Preprint Article Version 2 This version is not peer-reviewed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)

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 if L is not equal to NL, then P = NP. In addition, we show if L is equal to NL, then P = NP. In this way, we prove the complexity class P is equal to NP. Furthermore, we demonstrate the complexity class L is equal to NP.

Supplementary and Associated Material

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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