Formal Language Invariants of Finitely Generated Groups

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.