NP on Logarithmic Space

\(P\) 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 prove that \(NP \subseteq NSPACE(\log^{2} n)\) just using logarithmic space reductions.