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Some relatives of automatic and hyperbolic groups. (English) Zbl 1031.20047
Gomes, Gracinda M. S. (ed.) et al., Semigroups, algorithms, automata and languages. Proceedings of workshops held at the International Centre of Mathematics, CIM, Coimbra, Portugal, May, June and July 2001. Singapore: World Scientific. 379-406 (2002).
The authors define and examine hyperbolic, asynchronously automatic, and rational monoids. They consider the independence of the definitions from the generating set, some closure properties of the classes of asynchronously automatic and of hyperbolic monoids, the complexity of the word problem. They describe the relations between these classes of monoids.
For the entire collection see [Zbl 1005.00031].

20M05 Free semigroups, generators and relations, word problems
20F67 Hyperbolic groups and nonpositively curved groups