Mathematical Sciences: Group Theory and Formal Language Theory

这项研究是关于组合群论与自动机理论和形式语言之间的联系。主要研究人员将证明群的许多组合性质，例如具有自动结构或有理增长函数，可以用相应的具有某些附加性质的正则生成树的Cayley群来刻画。形式语言理论是由某些类型的机器确定的自由么半群的子集的理论。本研究关注形式语言理论与群体理论之间的互动关系。这项工作在群论和理论计算机科学中都很重要。

This research is concerned with the connections between combinatorial group theory and the theory of automata and formal languages. The principal investigator will show that many combinatorial properties of groups, such as having an automatic structure or a rational growth function, can be characterized in terms of the corresponding Cayley group possessing a regular spanning tree with certain additional properties. Formal language theory is the theory of subsets of free monoids which are determined by certain kinds of machines. This research is concerned with the interactions of formal language theory and group theory. This work is important both in group theory and in theoretical computer science.