A Geometric Characterization of Automatic Monoids
Pedro V. Silva · The Quarterly Journal of Mathematics · 2004
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.