Upper and Lower Bounds for Some Depth-3 Circuit Classes (1997)
| Venue: | In Proc. 12th Ann. IEEE Conf. Comput. Complexity Theory |
| Citations: | 8 - 1 self |
BibTeX
@INPROCEEDINGS{Beigel97upperand,
author = {Richard Beigel and Alexis Maciel},
title = {Upper and Lower Bounds for Some Depth-3 Circuit Classes},
booktitle = {In Proc. 12th Ann. IEEE Conf. Comput. Complexity Theory},
year = {1997},
pages = {580--584}
}
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Abstract
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 to a constant in the case where m is constant. We then use these upper bounds to derive exponential lower bounds for this class of circuits. In the unbounded m case, this yields a new proof of a lower bound of Grolmusz; in the constant m case, our result sharpens his lower bound. In addition, we prove an exponential lower bound if OR gates are also permitted on level two and m is a constant prime power. 1 Introduction About ten years ago, Furst, Saxe and Sipser [FSS] and Ajtai [Aj] showed that polynomialsize AC 0 circuits could not compute the parity function. It was hoped that this seminal result would be the first in a series of lower bounds for increasingly larger classes of circuits and that this would lead to th...
