NP on Logarithmic Space: Mediterranean International Conference of Pure & Applied Mathematics and Related Area (MICOPAM 2023)

01 September 2023, Version 3
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

The $P$ versus $NP$ problem 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 $DSPACE(S(n))$ and $NSPACE(S(n))$ for every space-constructible function $S(n)$. We prove that $NP \subseteq NSPACE(\log^{2} n)$ just using logarithmic space reductions.

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