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Automatic Groups and Knuth-Bendix with Infinitely Many Rules

D. B. A. Epstein·Paul J. Sanders
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Abstract

It is shown how to use a small finite state automaton in two variables in order to carry out part of the Knuth--Bendix process for rewriting words in a group. The main objective is to provide a substitute for the most space-demanding module of the existing software which attempts to find a shortlex-automatic structure for a group. 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. In our context this operation is vital. We point out a small potential improvement in the subset algorithm for making a non-deterministic automaton deterministic.

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D. B. A. Epstein, Paul J. Sanders. 1998-05-12. Automatic Groups and Knuth-Bendix with Infinitely Many Rules. https://arxiv.org/abs/math/9805057

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