D. B. A. Epstein, P. J. Sanders
Published 2000-01-06Version 1
It is shown how to use a small finite state automaton in two variables in order to carry out the Knuth-Bendix process for rewriting words in a group in shortlex order. The two-variable automaton can be used to store an infinite set of rules and to carry out fast reduction of arbitrary words using this infinite set. We introduce a new operation, which we call welding, which applies to an arbitrary finite state automaton. We show how to improve on the standard subset construction to determinize a non-deterministic automaton under special conditions which hold in our situation.
Comments: 63 pages, 6 figures. A completely rewritten version of math/9805057. A slightly shortened version of this paper has been accepted by IJAC
Algorithmically finite groups
Groups with undecidable word problem and almost quadratic Dehn function
Strong uniform expansion in $\mathrm{SL}(2,p)$
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