We investigate the complexity of depth-3 threshold circuits with majority gates at the output, possibly negated AND gates at level two, and MODm gates at level one. We show that the fan-in of the AND gates can be reduced to O(log n) in the case where m is unbounded, and ... more >>>

Continuing a line of investigation that has studied the function classes #P, #SAC^1, #L, and #NC^1, we study the class of functions #AC^0. One way to define #AC^0 is as the class of functions computed by constant-depth polynomial-size arithmetic circuits of unbounded fan-in addition and multiplication gates. In contrast to ... more >>>

We give an explicit construction of depth two threshold circuit with polynomial weights and $\tilde{O}(n^5)$ gates that computes an arbitrary threshold function. We also give the construction of such circuits with $O(n^3/\log n)$ gates computing the COMPARISON and CARRY functions, and that with $O(n^4/\log n)$ gates computing the ADDITION function. ... more >>>