P versus NP

Frank Vega (1)

1 Joysonic

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. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. Another major complexity classes are L, 1NL and NL. Whether L = NL is another fundamental question that it is as important as it is unresolved. We demonstrate the complexity class NL is equal to NP. This proof is based on NL is closed under 1NL-reductions: Specifically, when in the logarithmic space composition reduction of N(M(x)) on every input x, the Turing machine M is deterministic and N is nondeterministic in one way.

Mots clés: polynomial time; logarithmic space; complexity classes; one-way; completeness; reduction

Domaines: Complexité [cs.CC]

Frank Vega. P versus NP. 2020. ⟨hal-02199310v10⟩