Submitted:
26 November 2019
Posted:
29 November 2019
Read the latest preprint version here
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.
Keywords:
complexity classes
; completeness
; polynomial time
; reduction
; logarithmic space
; one-way
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