This paper presents an evolutionary developmental method for the design of arbitrarily growing sorting networks. The developmental model is based on a parallel rewriting system (a grammar) that is specified by an alphabet, an initial string (an axiom), and a set of rewriting rules. The rewriting process iteratively expands the axiom in order to develop more complex strings during a series of development steps (i.e., derivations in the grammar). A mapping function is introduced that allows for converting the strings onto comparator structures—building blocks of sorting networks. The construction of the networks is performed in such a way that a given (initial) sorting network grows progressively by adding further building blocks within each development step. For a given (fixed) alphabet, the axiom together with the rewriting rules themselves are the subjects of the evolutionary search. It will be shown that suitable grammars can be evolved for the construction of arbitrarily large sorting networks that grow with various given sizes of development steps. Moreover, the resulting networks exhibit significantly better properties (the number of comparators and delay) in comparison with those obtained by means of similar existing methods.

中文翻译：

---

通过重写系统的方式发展通用排序网络的进化发展

本文提出了一种设计任意增长排序网络的进化发展方法。发展模型基于由字母表、初始字符串（公理）和一组重写规则指定的并行重写系统（语法）。重写过程迭代地扩展公理，以便在一系列开发步骤（即语法中的推导）中开发更复杂的字符串。引入了映射函数，允许将字符串转换为比较器结构——排序网络的构建块。网络的构建以这样一种方式执行，即通过在每个开发步骤中添加更多构建块，给定（初始）排序网络逐渐增长。对于给定的（固定的）字母表，公理连同重写规则本身是进化搜索的主题。将会证明，可以进化出合适的语法来构建任意大的排序网络，这些网络随着各种给定大小的开发步骤而增长。此外，与通过类似现有方法获得的网络相比，由此产生的网络表现出明显更好的特性（比较器的数量和延迟）。