标题： 关于判别器克隆的运算等价性 显示英文标题

标题： Equivalence of operations with respect to discriminator clones

摘要： 对于集合 A 上的每个克隆 C，在 A 上的所有运算的集合上都有一种相关的等价关系，称为 C-等价，它将两个运算联系起来当且仅当每个运算都是用 C 中的运算作为替代实例得到的。本文证明了如果 C 是有限集上的辨别器克隆，那么只有有限个 C-等价类。此外，我们还表明最小的辨别器克隆在这个有限性性质方面是最小的。对于布尔函数的辨别器克隆，我们明确描述了相关的等价关系。 显示英文摘要

摘要： For each clone C on a set A there is an associated equivalence relation, called C-equivalence, on the set of all operations on A, which relates two operations iff each one is a substitution instance of the other using operations from C. In this paper we prove that if C is a discriminator clone on a finite set, then there are only finitely many C-equivalence classes. Moreover, we show that the smallest discriminator clone is minimal with respect to this finiteness property. For discriminator clones of Boolean functions we explicitly describe the associated equivalence relations.