P versus NP

EasyChair Preprint 3061, version 2

Abstract

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? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, 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 classes are L and NL. Whether L = NL is another fundamental question that it is as important as it is unresolved. We demonstrate that every problem in NP could be NL-reduced to another problem in L. In this way, we prove that every problem in NP is in NL with L Oracle. Moreover, we show the complexity class NP is equal to NL, since it is well-known that the logarithmic space oracle hierarchy collapses into NL.

Keyphrases: completeness, complexity classes, logarithmic space, one-way, polynomial time, reduction

@booklet{EasyChair:3061,
  author    = {Frank Vega},
  title     = {P versus NP},
  howpublished = {EasyChair Preprint 3061},
  year      = {EasyChair, 2020}}