Knuth-Bendix for groups with infinitely many rules
Group Theory
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0001035,
title = {Knuth-Bendix for groups with infinitely many rules},
author = {D. B. A. Epstein and P. J. Sanders},
journal= {arXiv preprint arXiv:math/0001035},
year = {2007}
}
Comments
63 pages, 6 figures. A completely rewritten version of math/9805057. A slightly shortened version of this paper has been accepted by IJAC