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On threshold circuits for parity

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2 Author(s)
Paturi, R. ; Dept. of Comput. Sci. & Eng., California Univ., San Diego, La Jolla, CA, USA ; Saks, Michael E.

Motivated by, the problem of understanding the limitations of neural networks for representing Boolean functions, the authors consider size-depth tradeoffs for threshold circuits that compute the parity function. They give an almost optimal lower bound on the number of edges of any depth-2 threshold circuit that computes the parity function with polynomially bounded weights. The main technique used in the proof, which is based on the theory of rational approximation, appears to be a potentially useful technique for the analysis of such networks. It is conjectured that there are no linear size, bounded-depth threshold circuits for computing parity

Published in:

Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on

Date of Conference:

22-24 Oct 1990