Mathematical Sciences: Presentations of Inverse Monoids

这项研究涉及到一种理论的发展 逆幺半群的表现形式。 一般有两个方面 将研究的问题。 第一个是关于 当一个逆幺半群是 由生成器和关系表示。 特别是，这个词 问题和E-酉问题将被研究，初始 重点集中在一个关系人的情况下。 许多几何 从组合群论以及基本的技术 将使用语言理论和自动机理论的结果。 第二个问题是关于封闭的研究。 自由逆幺半群的逆子幺半群 问题 特别是，封闭的 自由逆幺半群的逆子幺半群， 有限图，自由图的有理可识别子集 逆幺半群与有限非周期逆的点深度 monoid将被详细研究。 此外，一项尝试将 使之开始有限逆的计算理论 部分一一变换半群 这项研究涉及的理论幺半群，最简单的 上世纪引入的抽象代数对象。 调查人员特别感兴趣的是 这些结构正是在自动机理论中出现的， 计算机科学中的形式语言理论。 他们的技术 从群论到几何再到计算。 他们的 解决这些问题的方法是富有想象力的。 该提案 对数学和计算机都有重要贡献 科学

This research is concerned with the development of a theory of presentations of inverse monoids. There are two general areas of problems which will be studied. The first is concerned with basic decision problems which arise when an inverse monoid is presented by generators and relations. In particular, the word problem and the E-unitary problem will be studied, with initial emphasis focussed on the one relator case. Many of the geometric techinques from combinatorial group theory as well as basic results from language theory and automata theory will be used. The second problem is concerned with a study of the closed inverse submonoids of the free inverse monoid and related problems. In particular, the relationship between the closed inverse submonoids of a free inverse monoid, the topology of finite graphs, the rational and recognizable subsets of a free inverse monoid and the dot depth of a finite aperiodic inverse monoid will be studied in detail. In addition, an attempt will be made to begin a computational theory of finite inverse semigroups of partial one-one transformations. This research concerns the theory of monoids, the simplest of the abstract algebraic objects introduced in the last century. The particular ones that the investigators are interested in are precisely those structures arising in automata theory and the theory of formal languages in computer science. Their techniques range from group theory to geometry to computations. Their approaches to the problems are imaginative. This proposal should make important contributions to both mathematics and computer science.