I'm trying to prove $EXP \subset E^E$ (strictly).

I believe I need to construct my own $A \in E^E$ and show that $A \notin EXP$, but I cannot think of a smart way of doing that.



1 Answer 1


The class $E^E$ contains 2E, which is the class of problems solvable in iterated exponential time. The reason is that the E oracle can be applied on a padded input of exponential size. The time hierarchy theorem separates 2E from EXP.

  • $\begingroup$ To elaborate, are you saying we can express $E$ in terms of $DTIME(...)$ (i.e without an oracle), and show that it's strictly greater then $EXP=DTIME(2^{n^c})$? Because then, the conclusion comes directly from the time hierarchy theorem. $\endgroup$
    – galah92
    Commented Aug 1, 2018 at 10:20
  • $\begingroup$ Not exactly, though perhaps a more refined statement to that effect might hold. $\endgroup$ Commented Aug 1, 2018 at 10:42
  • $\begingroup$ Let us continue this discussion in chat. $\endgroup$
    – galah92
    Commented Aug 1, 2018 at 12:59

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