A catalogue of complete group presentations
Journal of Symbolic Computation
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Journal of Symbolic Computation
Computing shortest words via shortest loops on hyperbolic surfaces
Computer-Aided Design
On The Diversity Of Orderings On Strings
Fundamenta Informaticae
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Certain 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.