Formal Language Invariants of Finitely Generated Groups

在过去的几年中，对几何和语言理论方面的研究，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。 自动组的引入和上下文无关词问题的组分类是这一领域的重要发展。 形式语言对这种相互作用的贡献在于，它们提供了看待群的凯莱图几何的新方法。 这个建议的目标是进一步发展这种方法，通过描述其他类别的群体的语言理论属性。 这个项目是在群论和计算机辅助计算方面的一般领域这一领域。 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，代数对于算法的开发非常有用。 这项研究不仅有助于群论中计算机程序的发展，而且会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.