Šare的代数系统

M. Essert, D. Zubrinic
{"title":"Šare的代数系统","authors":"M. Essert, D. Zubrinic","doi":"10.32817/ams.2.1","DOIUrl":null,"url":null,"abstract":"We study algebraic systems MΓ of free semigroup structure, where Γ is a well ordered finite alphabet, discovered in 1970s within the Theory of Electric Circuits by Miro Šare, and and finding recent recent applications in Multivalued Logic, as well as in Computational Linguistics. We provide three simple axioms (reversion axiom (5) and two compression axioms (6) and (7)), which generate the corresponding equivalence relation between words. We also introduce a class of incompressible words, as well as the quotient Šare system MΓ~. The main result is contained in Theorem 16, announced by Šare without proof, which characterizes the equivalence of two words by means of Šare sums. The proof is constructive. We describe an algorithm for compression of words, study homomorphisms between quotient Šare systems for various alphabets Γ (Theorem 38), and introduce two natural Šare categories ŠŠa(M) and ŠŠa(M~). Šare systems are not inverse semigroups.","PeriodicalId":309225,"journal":{"name":"Acta mathematica Spalatensia","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Šare’s algebraic systems\",\"authors\":\"M. Essert, D. Zubrinic\",\"doi\":\"10.32817/ams.2.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study algebraic systems MΓ of free semigroup structure, where Γ is a well ordered finite alphabet, discovered in 1970s within the Theory of Electric Circuits by Miro Šare, and and finding recent recent applications in Multivalued Logic, as well as in Computational Linguistics. We provide three simple axioms (reversion axiom (5) and two compression axioms (6) and (7)), which generate the corresponding equivalence relation between words. We also introduce a class of incompressible words, as well as the quotient Šare system MΓ~. The main result is contained in Theorem 16, announced by Šare without proof, which characterizes the equivalence of two words by means of Šare sums. The proof is constructive. We describe an algorithm for compression of words, study homomorphisms between quotient Šare systems for various alphabets Γ (Theorem 38), and introduce two natural Šare categories ŠŠa(M) and ŠŠa(M~). Šare systems are not inverse semigroups.\",\"PeriodicalId\":309225,\"journal\":{\"name\":\"Acta mathematica Spalatensia\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta mathematica Spalatensia\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32817/ams.2.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta mathematica Spalatensia","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32817/ams.2.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

我们研究了自由半群结构的代数系统MΓ,其中Γ是一个有序的有限字母,在20世纪70年代由Miro Šare在电路理论中发现,并在多值逻辑以及计算语言学中找到了最近的应用。我们提供了三个简单公理(反转公理(5)和两个压缩公理(6)和(7)),它们产生了词之间相应的等价关系。我们还介绍了一类不可压缩词,以及商Šare系统MΓ~。主要的结果包含在Šare没有证明的定理16里,它用Šare和来表示两个词的等价。这个证明是建设性的。我们描述了一种单词压缩算法,研究了不同字母Γ的商Šare系统之间的同态(定理38),并引入了两个自然的Šare类别ŠŠa(M)和ŠŠa(M~)。Šare系统不是逆半群。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Šare’s algebraic systems
We study algebraic systems MΓ of free semigroup structure, where Γ is a well ordered finite alphabet, discovered in 1970s within the Theory of Electric Circuits by Miro Šare, and and finding recent recent applications in Multivalued Logic, as well as in Computational Linguistics. We provide three simple axioms (reversion axiom (5) and two compression axioms (6) and (7)), which generate the corresponding equivalence relation between words. We also introduce a class of incompressible words, as well as the quotient Šare system MΓ~. The main result is contained in Theorem 16, announced by Šare without proof, which characterizes the equivalence of two words by means of Šare sums. The proof is constructive. We describe an algorithm for compression of words, study homomorphisms between quotient Šare systems for various alphabets Γ (Theorem 38), and introduce two natural Šare categories ŠŠa(M) and ŠŠa(M~). Šare systems are not inverse semigroups.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信