Exponential hierarchy

In computational complexity theory, the exponential hierarchy is a hierarchy of complexity classes that is an exponential time analogue of the polynomial hierarchy. As elsewhere in complexity theory, “exponential” is used with 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. These hierarchies are sometimes also referred to as the weak exponential hierarchies, to differentiate them from the strong exponential hierarchy, which contains both of the weak hierarchies.