1
$\begingroup$
  • 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 $NL^2 = coNL^2$

$\endgroup$

1 Answer 1

2
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.