Semigroups, Formal Languages and Computation

主要结果如下：（1）广义逆[*-]半群类具有强合并性质。（2）利用右ω-陪集刻画了广义逆 *-半群的传递表示。(3)We得到了完全0-单半群是特殊合并基的充要条件。（4）有限半群是否具有表示扩张性质的判定问题是可判定的。（5）得到了语言的混洗剩余的几个性质和一个特征。例如，最大语言的洗牌剩余等于一个给定的语言的存在条件。(6)我们得到了具体的描述自由代数的几个品种所提供的语言结构配备了操作的逆转，连接，洗牌和其他。

The main results of this project are as follows :(1)The class of generalized inverse [*-]semigroups has the strong amalgamation property.(2)The transitive representations of a generalized inverse *-semigroup is characterized by using right ω-cosets.(3)We obtained the necessary and sufficient conditions for that a completely 0-simple semigroup is a special amalgamation base.(4)The decision problem whether or not a finite semigroup has representation extension property is decidable.(5)Several properties and a characterization of the shuffle residual of a language are obtained. For example, conditions for the existence of maximal languages whose shuffle residual equals a given language are obtained.(6) We obtained concrete descriptions of the free algebras in several varieties given by language structures equipped with the operations of reversal, concatenation, shuffle and others.