Sparse Complete Sets for coNP: Solution of the P Versus NP Problem

EasyChair Preprint 6893, version 1

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? 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. In 1979, Fortune showed that if any sparse language is coNP-complete, then P = NP. We prove there is a possible sparse language in coNP-complete. In this way, we demonstrate the complexity class P is equal to NP.

Keyphrases: Complement Language, completeness, complexity classes, polynomial time, sparse

@booklet{EasyChair:6893,
  author    = {Frank Vega},
  title     = {Sparse Complete Sets for coNP: Solution of the P Versus NP Problem},
  howpublished = {EasyChair Preprint 6893},
  year      = {EasyChair, 2021}}