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The Quarterly Journal of Mathematics 2004 55(3):333-356; doi:10.1093/qmath/hah006
© 2004 by Oxford University Press
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A Geometric Characterization of Automatic Monoids

Pedro V. Silva1 and Benjamin Steinberg2

1 Centro de Matemática, Faculdade de Ciências, Universidade do Porto, R. Campo Alegre, 687 4169-007 Porto, Portugal 2 School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada

It is well known that automatic groups can be characterized using geometric properties of their Cayley graphs. Along the same line of thought, we provide a geometric characterization of automatic monoids. This involves working with a slightly strengthened definition of an automatic monoid which is still a proper generalization of the concept of an automatic group. The two definitions coincide in the case of right cancellative monoids for which a particularly simple characterization is obtained.

Received 9 May 2001. Revised 21 December 2003.


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