Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number. The assembly index is determined by the minimal number of recursive joining operations necessary to construct an object from basic parts, and the copy number is how many of the given object(s) are observed. Together these allow defining a quantity, called Assembly, which captures the amount of causation required to produce the observed objects in the sample. AT's focus on how selection generates complexity offers a distinct approach to that of computational complexity theory which focuses on minimum descriptions via compressibility. To explore formal differences between the two approaches, we show several simple and explicit mathematical examples demonstrating that the assembly index, itself only one piece of the theoretical framework of AT, is formally not equivalent to other commonly used complexity measures from computer science and information theory including Huffman encoding and Lempel-Ziv-Welch compression.

翻译：装配理论（AT）通过装配方程量化选择过程，并基于装配指数和拷贝数这两个度量指标识别大量存在的复杂对象。装配指数由从基本部件构建对象所需的最小递归连接操作数决定，拷贝数则表征给定对象被观测到的数量。二者共同定义了一个称为"装配量"的物理量，该量反映了产生样本中观测对象所需的因果作用量。AT关注选择如何生成复杂性，这与计算复杂度理论通过可压缩性关注最小描述的方法形成鲜明对比。为探究两种方法的形式差异，我们通过若干简洁的数学实例证明：作为AT理论框架组成部分的装配指数，在形式上并不等同于计算机科学与信息论中常用的其他复杂度度量（包括霍夫曼编码和Lempel-Ziv-Welch压缩算法）。