Knuth-Bendix for groups with infinitely many rules

Details Knuth-Bendix for groups with infinitely many rules Knuth-Bendix for groups with infinitely many rules

2000-01-06

arxiv.org/abs/math/0001035v1

Mathematics

Group Theory

63 pages, 6 figures. A completely rewritten version of math/9805057. A slightly shortened version of this paper has been accep

Scientific paper

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.

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