$L$ is unequal $NL$ under the Strong Exponential Time Hypothesis

Reiner Czerwinski

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arXiv · 2305.02271

$L$ is unequal $NL$ under the Strong Exponential Time Hypothesis

Reiner Czerwinski

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Abstract

Due to Savitch's theorem we know $NL\subseteq DSPACE(\log^2(n))$. To show this upper bound, Savitch constructed an algorithm with $O(\log^2(n))$ space on the working tape. We will show that Savitch's algorithm also described a lower bound under the Strong Exponential Time Hypothesis. Every algorithm for the Connectivity Problem needs $O(\log^2(n))$ space in this case.

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Reiner Czerwinski. 2023-04-01. $L$ is unequal $NL$ under the Strong Exponential Time Hypothesis. https://arxiv.org/abs/2305.02271

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