Richard Beigel, Alexis Maciel

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 ...
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Manindra Agrawal, Eric Allender, Samir Datta

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 ...
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Kazuyuki Amano, Akira Maruoka

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 >>>

Mark Bun, Justin Thaler

We prove two new results about the inability of low-degree polynomials to uniformly approximate constant-depth circuits, even to slightly-better-than-trivial error. First, we prove a tight $\tilde{\Omega}(n^{1/2})$ lower bound on the threshold degree of the Surjectivity function on $n$ variables. This matches the best known threshold degree bound for any AC$^0$ ... more >>>