P versus NP

2018-04-25T16:42:27Z (GMT) by 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? This question was first mentioned in a letter written by John Nash to the National Security Agency in 1955. 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 Sharp-P. Whether P = Sharp-P is another fundamental question that it is as important as it is unresolved. If any single Sharp-P-complete problem can be solved in polynomial time, then every NP problem has a polynomial time algorithm. The problem Sharp-MONOTONE-2SAT is known to be Sharp-P-complete. We prove Sharp-MONOTONE-2SAT is in P. In this way, we demonstrate the P versus NP problem.