P versus NP

Abstract

P versus N P 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 N P ? The precise statement of the P versus N P 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 P-Sel. P-Sel is the class of decision problems for which there is a polynomial time algorithm (called a selector) with the following property: Whenever it's given two instances, a "yes" and a "no" instance, the algorithm can always decide which is the "yes" instance. It is known that if N P