Impossibility Results for Threshold Networks
نویسندگان
چکیده
It is shown that a threshold network of width w and depth d cannot be constructed from balancers of width p0; p1; : : : ; pm 1, if w does not divide P , where P is the least common multiple of p0; p1; : : : ; pm 1. This holds regardless of the size of the network, as long as it is nite, and it implies a lower bound of logP w on the depth of the network. More strongly, a lower bound of logpmax w is shown on the length of every path from an input wire to a certain output wire that exhibits the threshold property, where pmax is the maximum among p0; p1; : : : ; pm 1
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