Abstract
We introduce a notion of hyperbolicity in monoids which is a restriction of that suggested by Duncan and Gilman. One advantage is that the notion gives rise to efficient algorithms for dealing with certain questions; for example, the word problem can be solved in time O ( n log n ) . We also introduce a new way of defining automatic monoids which provides a uniform framework for the discussion of these concepts. Hyperbolic monoids (in the sense introduced here) turn out to be biautomatic.
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