Who introduced the complexity class AC? I taught $AC^0$ lower bounds today, and one of the students asked about the reason for the name $AC$.
The official explanation is that the "A" stands for "Alternation".

I vaguely remember being told many years ago that Nick Pippenger Steve Cook named $NC$ after Nick Pippenger (Nick's class), and later Nick named $SC$ after Steve (Steve's class). 

The $NC$ part of the story is documented, e.g., in Wikipedia and in the complexity zoo, the story for $SC$ is told here. 

I wonder whether $AC$ has a similar history, but I couldn't find any reference to $AC$'s inventor.

Does someone know who defined $AC$?
I believe that the notation AC first appears in Cook's "A Taxonomy of Problems with Fast Parallel Algorithms" from 1985. On page 11 (page 12 of the journal) we read:


  To state a more general form of this result we introduce the following terminology.
  
  Definition. $AC^k$, for $k=1,2,\ldots$, is the class of problems solvable by an ATM in space $O(\log n)$ and alternation depth $O(\log^k n)$.


This class is actually a uniform version of AC.

There follows an alternative characterization by Ruzzo and Tompa, appearing in a technical report by Stockmeyer and Vishkin, and later on in "Constant depth reducibility" by Chandra, Stockmeyer and Vishkin from 1984. They use the notation SIZE-DEPTH(poly, constant) (see page 3).

Cook goes on to mention another unpublished characterization by himself and Ruzzo. Further results due to Ruzzo are mentioned, including $AC^k \subseteq NC^{k+1}$ ("On uniform circuit complexity", Ruzzo, 1981). The latter paper (as well as Ruzzo's earlier paper also mentioned) doesn't contain the notation AC, but rather a myriad of other notations, emphasizing the notion of uniformity used.

All these papers mention alternating Turing machines a lot, giving credence to the hypothesis that A stands for alternating.