The use of Knuth-Bendix methods to solve the wordproblem in automatic groups

AbstractCertain classes of infinite groups arising from geometry and topology are known to have solvable word problem. We describe the development of practical methods for the solution of the word problem based on the reduction of words in the generators to a normal form. The Knuth-Bendix completion procedure is the principal tool used but, in the case that this process does not halt, we use alternative methods involving the construction of finite-state automata. A computer implementation of these procedures together with some performance statistics on some simple examples are also described