Exponential hierarchy

In computational complexity theory, the exponential hierarchy is a hierarchy of complexity classes, which is an exponential time analogue of the polynomial hierarchy. As elsewhere in complexity theory, “exponential” is used in two different meanings (linear exponential bounds ${\displaystyle 2^{cn}}$ for a constant c, and full exponential bounds ${\displaystyle 2^{n^{c}}}$), leading to two versions of the exponential hierarchy:

We have E ⊆ NE ⊆ EH ⊆ ESPACE, EXP ⊆ NEXP ⊆ EXPH ⊆ EXPSPACE, and EH ⊆ EXPH.

Complexity Zoo: Class EH

...
Wikipedia