A note on a theorem of Barrington, Straubing and Thérien

We show that the result of Barrington, Straubing and Thérien (1989) provides, as a direct corollary, an exponential lower bound for the size of depth-two MOD 6 circuits computing the AND function. This problem was solved, in a more general way, by Krause and Waack (1991). We point out that all known lower bounds rely on the special form of the MOD 6 gate occurring at the bottom of the circuits, so that in fact, proving a lower bound for “general” MOD 6 circuits of depth two is still an open question.