Groups, languages, and automata / Derek F. Holt, University of Warwick, Sarah Rees, University of Newcastle upon Tyne, Claas E. R©œver, National University of Ireland, Galway

Includes bibliographical references and indexes

Part one. Introduction. Group theory ; Formal languages and automata theory ; Introduction to the word problem -- Part two. Finite state automaata and groups. Rewriting systems ; Automatic groups ; Hyperbolic groups ; Geodesics ; -- Subgroups and coset systems ; Automata groups -- Part three. The word problem. Solubility of the word problem ; Context-free and one-counter word problems ; Context-sensitive problems ; Word problems in other language classes ; The co-word problem and the conjugacy problem.

Many connections exist between group theory and automata theory, and a wide variety of them are discussed in this text. Any necessary background material is provided, and connections are explored along a number of strands that lead to the forefront of current research in geometric group theory.