Download PDFOpen PDF in browserCurrent versionNP on Logarithmic SpaceEasyChair Preprint 9555, version 98 pages•Date: July 21, 2023AbstractP 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 prove that if L = NL, then every NP problem is in L with oracle access to L. This means that proving the separation from NP to L is as hard as proving that L is not equal to NL. Keyphrases: completeness, complexity classes, logarithmic space, polynomial time, reduction
