On Lower Bounds for the Depth of Threshold Circuits with Weights from {-1, 0, +1}

We consider boolean threshold circuits of polynomial size and constant depth. The threshold gates are of unbounded fan-in and with weights from {−1,0, +1}. We introduce the notation of sharp bounded density and prove that boolean functions f n (x) satisfying this property cannot be realized by threshold circuits of depth two with weights from {−1,0,+1}. Furthermore, some properties of threshold circuits are discussed resulting in lower bounds of depth four.

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