Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The complexity of multilayer $d$-dimensional circuits   In this paper we research a model of multilayer circuits with a single
logical layer. We consider $\lambda$-separable graphs as a support for
circuits. We establish the Shannon function lower bound $\max
\bigl(\frac{2^n}{n}, \frac{2^n (1 - \lambda)}{\log k} \bigr)$ for this type of
circuits where $k$ is the number of layers. For $d$-dimensional graphs, which
are $\lambda$-separable for $\lambda = \frac{d - 1}{d}$, this gives the Shannon
function lower bound $\frac{2^n}{\min(n, d \log k)}$. For multidimensional
rectangular circuits the proved lower bound asymptotically matches to the upper
bound.

36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol