There is a newer version of this record available.

Preprint Open Access

On P versus NP

Frank Vega

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
Files (198.2 kB)
Name Size
onpversusnp.pdf
md5:625568cc9d926cc59b8675ecc35a1c2d
198.2 kB Download
1,004
514
views
downloads
All versions This version
Views 1,00470
Downloads 51418
Data volume 97.4 MB3.6 MB
Unique views 82365
Unique downloads 41016

Share

Cite as