集中独偶群和目击者的数量

2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL) Pub Date : 2017-05-01 DOI:10.1109/ISMVL.2017.34

Hajime Machida, I. Rosenberg

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引用次数: 3

摘要

考虑在固定有限集合a上定义的多变量函数。一个集中一元群M是A上的一元函数的集合，它与A上某个函数集合F的所有成员交换。集合F称为M的一个见证。我们证明了每个集中一元群都有一个见证，其奇异度不超过|A|。接下来，我们给出了在一个三元集合上的一元群集中的例子，这些集合有向量3的见证，但没有向量2的见证。

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Centralizing Monoids and the Arity of Witnesses

Multi-variable functions defined over a fixed finite set A are considered. A centralizing monoid M is a set of unary functions on A which commute with all members of some set F of functions on A. The set F is called a witness of M. We show that every centralizing monoid has a witness whose arity does not exceed |A|. Next, we present examples of centralizing monoids on a three-element set which have witnesses of arity 3 but do not have witnesses of arity 2.

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2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)

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