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.
| Name | Size | |
|---|---|---|
|
onpversusnp.pdf
md5:fe4d2740a0271b40bb410aa26eb644d2 |
201.8 kB | Download |
| All versions | This version | |
|---|---|---|
| Views | 1,005 | 35 |
| Downloads | 519 | 16 |
| Data volume | 98.3 MB | 3.2 MB |
| Unique views | 824 | 30 |
| Unique downloads | 414 | 13 |
- Publication date:
- March 17, 2019
- DOI:
-
- Keyword(s):
- P NP coNP coNP-complete Minimum Boolean circuit
- License (for files):
- Creative Commons Attribution 4.0 International