10.5281/zenodo.2596354
https://zenodo.org/records/2596354
oai:zenodo.org:2596354
Frank Vega
Frank Vega
0000-0001-8210-4126
Joysonic
On P versus NP
Zenodo
2019
P
NP
coNP
coNP-complete
Minimum
Boolean circuit
2019-03-17
10.5281/zenodo.2588891
Creative Commons Attribution 4.0 International
P versus NP is considered as one of the great open problems of science. This consists in knowing the answer of the following question: Is P equal to NP? This problem was first mentioned in a letter written by John Nash to the National Security Agency in 1955. 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 huge problem have failed. Another major complexity class is coNP. Whether NP = coNP is another fundamental question that it is as important as it is unresolved. To attack the P versus NP problem, the concept of coNP-completeness is very useful. We prove there is a problem in coNP-complete that is not in P. In this way, we show that P is not equal to coNP. Since P = NP implies P = coNP, then we also demonstrate that P is not equal to NP.
Archived previous version in https://hal.archives-ouvertes.fr/hal-01509423