Kleene代数及相关半模结构

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 Algebras and Some Related Semimodules

Kleene algebra is fundamental and ubiquitous in computer science.Kleene modules, Boolean modules,dynamic algebras and other closely related algebraic structures are useful for reasoning about programs.In this paper,Kleene algebras,Kleene modules,inductive *-semirings 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.