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 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. We prove there is a problem in coNP 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 (162.1 kB)
Name Size
onpversusnp.pdf
md5:c704c3d2c0d3bd5045ea4f845afa91e4
162.1 kB Download
843
464
views
downloads
All versions This version
Views 843107
Downloads 46466
Data volume 88.0 MB10.7 MB
Unique views 663102
Unique downloads 36161

Share

Cite as