L is unequal NL under the Strong Exponential Time Hypothesis

04/01/2023

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by   Reiner Czerwinski, et al.

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Due to Savitch's theorem we know NL⊆ 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.