The $\textit{von Neumann Computer Architecture}$ has a distinction between computation and memory. In contrast, the brain has an integrated architecture where computation and memory are indistinguishable. Motivated by the architecture of the brain, we propose a model of $\textit{associative computation}$ where memory is defined by a set of vectors in $\mathbb{R}^n$ (that we call $\textit{anchors}$), computation is performed by convergence from an input vector to a nearest neighbor anchor, and the output is a label associated with an anchor. Specifically, in this paper, we study the representation of Boolean functions in the associative computation model, where the inputs are binary vectors and the corresponding outputs are the labels ($0$ or $1$) of the nearest neighbor anchors. The information capacity of a Boolean function in this model is associated with two quantities: $\textit{(i)}$ the number of anchors (called $\textit{Nearest Neighbor (NN) Complexity}$) and $\textit{(ii)}$ the maximal number of bits representing entries of anchors (called $\textit{Resolution}$). We study symmetric Boolean functions and present constructions that have optimal NN complexity and resolution.

翻译：$\textit{冯·诺伊曼计算机体系结构}$将计算与存储相区分。相比之下，大脑采用一体化架构，其中计算与存储不可区分。受大脑架构启发，我们提出一种$\textit{联想计算}$模型：存储由$\mathbb{R}^n$中的一组向量（称为$\textit{锚点}$）定义，计算通过从输入向量收敛至最近邻锚点完成，输出则是与该锚点关联的标签。具体而言，本文研究布尔函数在联想计算模型中的表示问题，其中输入为二进制向量，对应输出为最近邻锚点的标签（$0$或$1$）。该模型中布尔函数的信息容量与两个量相关：$\textit{(i)}$ 锚点数量（称为$\textit{最近邻复杂度}$）和 $\textit{(ii)}$ 锚点条目表示的最大比特数（称为$\textit{分辨率}$）。我们重点研究对称布尔函数，并给出具有最优最近邻复杂度和分辨率的构造方案。