Notions of hyperbolicity in monoids

Authors:
Michael Hoffmann;Richard M. Thomas
Affiliations:
Department of Computer Science, University of Leicester, Leicester LE1 7RH, UK;Department of Computer Science, University of Leicester, Leicester LE1 7RH, UK
Venue:
Theoretical Computer Science
Year:
2010

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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(nlogn). 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.