What is consequences of $PH\subseteq NSPACE((\log n)^2)$?

We don't even know PH is equals to L or not. I am wondering what will be happened when $PH\subseteq NSPACE((\log n)^2)$?

  • 1
    $\begingroup$ For $NP \subseteq NSPACE((\log(n)^2)$, it contredicts the ETH, since it implies that all $NP$ problem can be solve in $n^{\log(n)}$ times. From cstheory.stackexchange.com/questions/36750/… you get that Exp-time hiearchy collapse at the second level. $\endgroup$ – C.P. Jul 28 '18 at 10:31

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.