Kleene代数及相关半模结构  

Kleene Algebras and Some Related Semimodules

作　　者：柳晓燕[1] 冯锋[1] 

机构地区：[1]西安邮电学院理学院,陕西西安710121

出　　处：《数学的实践与认识》2010年第11期198-205,共8页Mathematics in Practice and Theory

基　　金：陕西省教育厅科研计划项目(08JK432;09JK722;09JK724;09JK728)

摘　　要：Kleene代数在理论计算机科学中具有基础而特殊的重要性，Kleene模、布尔模和动态代数等与Kleene代数密切相关的半模结构在程序的语义逻辑及推理中发挥着十分重要的作用．将半环和半模等代数系统作为基本构架，研究了理论计算机科学中的Kleene代数、Kleene模和归纳＊-半环等重要概念，并将这些对象统一为序＊-半环上称为归纳半模的代数结构．进一步，提出并讨论了弱归纳半模、伪归纳半模以及伪弱归纳半模等相关概念．Kleene algebra is fundamental and ubiquitous in computer science. Kleene mod- ules, Boolean modules, dynamic algebras and other closely related algebraic structures are useful for reasoning about programs. In this paper, Kleene algebras, Kleene modules, in- ductive ＊-sernirings and some relevant notions, which play an important role in theoretical computer science are investigated in a framework of semirings and semimodules. As common generalizations of these important concepts, the notions of inductive semimodules, weak inductive semimodules, pseudo inductive semimodules and pseudo weak inductive semimodules are introduced and related properties are discussed.

关 键 词：半环 半模 Kleene代数 Kleene模 归纳半模 

分 类 号：O153.3[理学—数学]