• From Savitch's theorem we have $NL^2 \subseteq L^4$, which is deterministic and thus closed under complement.
  • From Immerman–Szelepcsényi theorem we have $NL = coNL$.

Why then $NL^2 = coNL^2$


1 Answer 1


The Immerman–Szelepcsényi theorem states that $\mathsf{NSPACE}(s(n))$ is closed under complementation whenever $s(n) \geq \log n$.


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