Formal Language Invariants of Finitely Generated Groups

在过去的几年里，对有限呈现群的几何和语言理论方面的研究已经在群论、几何、自动机理论和形式语言之间产生了显著的相互作用。自动分组的引入和无上下文词问题分组的分类是该领域的重要进展。形式语言对这种相互作用的贡献在于，它们提供了观察群的凯利图几何的新方法。本提案的目标是进一步发展这一方法，根据语言理论的性质来描述其他类别的群体。这个项目是在群论和这个领域的计算机辅助计算方面的一般领域。人们对使用计算机来回答代数中的理论问题越来越感兴趣，相反，代数对算法的发展非常有用。本研究不仅有助于群论计算机程序的发展，而且将影响其他领域计算机程序的发展。

In the past several years investigation of geometric and language-theoretic aspects of finitely presented groups has engendered a remarkable interplay between group theory, geometry, and the theory of automata and formal languages. The introduction of automatic groups and the classification of groups with context free word problem are significant developments in this area. The contribution of formal languages to this interplay is that they afford new ways of looking at the geometry of Cayley diagrams of groups. The goal of this proposal is to develop this approach further by characterizing other classes of groups in terms of the language-theoretic properties. This project is in the general area of group theory and the computer-aided computational aspects of this field. There is a growing interest in using computers to answer theoretical questions in algebra and conversely, algebra is quite useful for the development of algorithms. This research will not only aid in the development of computer programs in group theory but will influence the development of computer programs in other areas.