{"title":"Centralizing Monoids and the Arity of Witnesses","authors":"Hajime Machida, I. Rosenberg","doi":"10.1109/ISMVL.2017.34","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":393724,"journal":{"name":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2017.34","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
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.