%0 DATA
%A Frank, Vega
%D 2017
%T P versus NP on NP-completeness
%U https://figshare.com/articles/P_versus_NP_on_NP-completeness/5709676
%R 10.6084/m9.figshare.5709676.v1
%2 https://ndownloader.figshare.com/files/10014685
%K Complexity Classes
%K Completeness
%K Theory of Numbers
%K Polynomial Time
%K Certificate
%X 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? This question 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 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 NP-complete. To attack the P versus NP question the concept of NP-completeness has been very useful. We prove some interesting results regarding this class which affect directly to the P versus NP problem. Indeed, this study provides true facts that might address to think in the possibility of a definitely P = NP answer.