There is a newer version of this record available.

Preprint Open Access

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 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. To attack the P versus NP problem, the NP-completeness is a useful tool. We prove the known NP-complete problem MONOTONE 1-IN-3 3SAT can be polynomially reduced to the polynomial language 2SET PACKING. In this way, MONOTONE 1-IN-3 3SAT must be in P. If any NP-complete problem can be solved in polynomial time, then every language in NP has a polynomial time algorithm. Hence, we demonstrate the complexity class P is equal to NP.

Files (254.1 kB)
Name Size
manuscript.pdf
md5:ae0aa36585e165e638c39d82f931d41d
254.1 kB Download
124
89
views
downloads
All versions This version
Views 1247
Downloads 897
Data volume 22.6 MB1.8 MB
Unique views 1006
Unique downloads 686

Share

Cite as