The name "AC" was chosen by analogy to
NC, with the "A" in the name standing for "alternating" and referring both to the alternation between the AND and OR gates in the circuits and to
alternating Turing machines.[1]
The smallest AC class is
AC0, consisting of constant-depth unlimited fan-in circuits.
The total hierarchy of AC classes is defined as
Relation to NC
The AC classes are related to the
NC classes, which are defined similarly, but with gates having only constant fanin. For each i, we have[2][3]
As an immediate consequence of this, we have that NC = AC.[4]
It is known that inclusion is strict for i = 0.[3]
Variations
The power of the AC classes can be affected by adding additional gates. If we add gates which calculate the
modulo operation for some modulus m, we have the classes
ACCi[m].[4]