The complexity of multilayer d-dimensional circuits
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In this paper we research a model of multilayer circuits with a single logical layer. We consider λ-separable graphs as a support for circuits. We establish the Shannon function lower bound max(2^n/n, 2^n (1 - λ)/log k) for this type of circuits where k is the number of layers. For d-dimensional graphs, which are λ-separable for λ = d - 1/d, this gives the Shannon function lower bound 2^n/min(n, d log k). For multidimensional rectangular circuits the proved lower bound asymptotically matches to the upper bound.
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