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

April 01, 2023 · The Ethereal · 🏛 arXiv.org

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Authors Reiner Czerwinski arXiv ID 2305.02271 Category cs.CC: Computational Complexity Cross-listed cs.DS Citations 0 Venue arXiv.org Last Checked 3 months ago
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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