关于克隆的操作的等效性
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存在相关联的等价关系，称为C-等价，它关联两个运算当且仅当每个运算都是另一个运算的替换实例，使用来自C的运算。本文证明了：如果C是有限集上的一个C-克隆，则C-等价类的个数只有1/2。此外，我们表明，最小的克隆是最小的有限性。对于布尔函数的双克隆，我们明确地描述了相关的等价关系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
