It is known that $EXP$ doesn't have circuits of size $n^k$. On the other hand proving $10 n$ lower bound on circuit size for $E$, $NE$ or even $E^{NP}$ is a known open problem.

My question is following: do we know any non-trivial lower bounds for any of the following classes?

  • $Time(2^{n \sqrt{\log(n)}})$
  • $NTime(2^{n \sqrt{\log(n)}})$
  • $Time(2^{n \sqrt{\log(n)}})^{NP}$

Instead of $n \sqrt{\log(n)}$ could be any function in $o(n \log{n})$. After $n \log{n}$ the straightforward diagonalization should start working.


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.