10.5281/zenodo.1438974
https://zenodo.org/records/1438974
oai:zenodo.org:1438974
Frank Vega
Frank Vega
0000-0001-8210-4126
Joysonic
UP versus NP
Zenodo
2018
Polynomial Time
UP
NP
Quadratic Congruences
NP-complete
2018-09-23
10.5281/zenodo.1433418
Creative Commons Attribution 4.0 International
UP versus NP
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? A precise statement of the P versus NP problem was introduced independently in 1971 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 UP. Whether UP = NP is another fundamental question that it is as important as it is unresolved. To attack the UP = NP question the concept of NP-completeness is very useful. If any single NP-complete problem is in UP, then UP = NP. Quadratic Congruences is a well-known NP-complete problem. We prove Quadratic Congruences is also in UP. In this way, we demonstrate that UP = NP.