‘Context-free rewriting systems and word-hyperbolic structures with uniqueness’
[with V. Maltcev]
International Journal of Algebra and Computation, 22, no. 7 (2012).
DOI: 10.1142/S0218196712500610. MR: 2999367. ZBL: 1284.68320.

Abstract

This paper proves that any monoid presented by a confluent context-free monadic rewriting system is word-hyperbolic. This result then applied to answer a question asked by Duncan & Gilman by exhibiting an example of a word-hyperbolic monoid that does not admit a word-hyperbolic structure with uniqueness (that is, in which the language of representatives maps bijectively onto the monoid).