Preprint Open Access

Sparse complete sets for coNP: Solution of the P versus NP problem

Frank Vega

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 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.

Files (324.8 kB)
Name Size
manuscript.pdf
md5:78011b7805d46a02f91dffc0e8024c12
324.8 kB Download
126
86
views
downloads
All versions This version
Views 12631
Downloads 8615
Data volume 22.6 MB4.9 MB
Unique views 9630
Unique downloads 6115

Share

Cite as