**AC**^{0} is a complexity class used in circuit complexity. It is the smallest class in the AC hierarchy, and consists of all families of circuits of depth O(1) and polynomial size, with unlimited-fanin AND gates and OR gates. (We allow NOT gates only at the inputs). It thus contains **NC**^{0}, which has only bounded-fanin AND and OR gates.

Integer addition and subtraction are computable in AC^{0}, but multiplication is not (at least, not under the usual binary or base-10 representations of integers).

From a descriptive complexity viewpoint, DLOGTIME-uniform AC^{0} is equal to the descriptive class FO+BIT of all languages describable in first-order logic with the addition of the BIT predicate, or alternatively by FO(+, ×), or by Turing machine in the logarithmic hierarchy.

In 1984 Furst, Saxe, and Sipser showed that calculating the parity of an input cannot be decided by any AC^{0} circuits, even with non-uniformity. It follows that AC^{0} is not equal to NC^{1}, because a family of circuits in the latter class can compute parity. More precise bounds follow from switching lemma. Using them, it has been shown that there is an oracle separation between the polynomial hierarchy and PSPACE.