P versus NP

EasyChair Preprint 3061, version 8

Abstract

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? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. 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. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. Another major complexity class is Sharp-P-complete. A polynomial time algorithm for solving a Sharp-P-complete problem, if it existed, then this would solve the P versus NP problem by implying that P and NP are equal. We demonstrate there is a problem in Sharp-P-complete that can be solved in polynomial time. In this way, we prove the complexity class P is equal to NP.

Keyphrases: completeness, complexity classes, logarithmic space, one-way, polynomial time, reduction

@booklet{EasyChair:3061,
  author    = {Frank Vega},
  title     = {P versus NP},
  howpublished = {EasyChair Preprint 3061},
  year      = {EasyChair, 2020}}