Download PDFOpen PDF in browserCurrent versionSparse Complete Sets for coNP: Solution of the P Versus NP ProblemEasyChair Preprint 6893, version 111 pages•Date: October 19, 2021AbstractP 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 coNPcomplete, then P = NP. We prove there is a possible sparse language in coNPcomplete. In this way, we demonstrate the complexity class P is equal to NP. Keyphrases: Complement Language, completeness, complexity classes, polynomial time, sparse
