{"title":"极大部分克隆的极小覆盖","authors":"Karsten Schölzel","doi":"10.1109/ISMVL.2009.32","DOIUrl":null,"url":null,"abstract":"A partial function f on a k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≫= 3 there exists a unique minimal covering.","PeriodicalId":115178,"journal":{"name":"2009 39th International Symposium on Multiple-Valued Logic","volume":"48 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Minimal Coverings of Maximal Partial Clones\",\"authors\":\"Karsten Schölzel\",\"doi\":\"10.1109/ISMVL.2009.32\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A partial function f on a k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≫= 3 there exists a unique minimal covering.\",\"PeriodicalId\":115178,\"journal\":{\"name\":\"2009 39th International Symposium on Multiple-Valued Logic\",\"volume\":\"48 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 39th International Symposium on Multiple-Valued Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISMVL.2009.32\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 39th International Symposium on Multiple-Valued Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISMVL.2009.32","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A partial function f on a k-element set Ek is a partial Sheffer function if every partial function on Ek is definable in terms of f. Since this holds if and only if f belongs to no maximal partial clone on Ek, a characterization of partial Sheffer functions reduces to finding families of minimal coverings of maximal partial clones on Ek. We show that for each k ≫= 3 there exists a unique minimal covering.
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