Abstract
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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Albrecht, A. (1995). On lower bounds for the depth of threshold circuits with weights from {−1,0,+1}. In: Jantke, K.P., Lange, S. (eds) Algorithmic Learning for Knowledge-Based Systems. Lecture Notes in Computer Science, vol 961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60217-8_19
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DOI: https://doi.org/10.1007/3-540-60217-8_19
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