@article{77129b1dea80453da7461fce4e6cfaf4,
title = "Algorithmic properties of inverse monoids with hyperbolic and tree-like Sch{\"u}tzenberger graphs",
abstract = "We prove that the class of finitely presented inverse monoids whose Sch{\"u}tzenberger graphs are quasi-isometric to trees has a uniformly solvable word problem, furthermore, the languages of their Sch{\"u}tzenberger automata are context-free. On the other hand, we show that there is a finitely presented inverse monoid with hyperbolic Sch{\"u}tzenberger graphs and an unsolvable word problem.",
keywords = "Context-free language, Finitely presented inverse monoid, Hyperbolic group, Tree-like inverse monoid, Virtually free group, Word problem",
author = "Gray, {Robert D.} and Silva, {Pedro V.} and N{\'o}ra Szak{\'a}cs",
note = "Funding information: The second author was partially supported by CMUP, which is financed by national funds through FCT – Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia, I.P., under the project with reference UIDB/00144/2020. The third author was funded by the European Union's Horizon 2020 research and innovation programme under the Marie Sk{\l}odowska-Curie grant agreement No. 799419. The third author was partially supported by the Hungarian National Foundation for Scientific Research grant nos. K115518 and K128042.",
year = "2022",
month = dec,
day = "1",
doi = "10.1016/j.jalgebra.2022.07.029",
language = "English",
volume = "611",
pages = "651--687",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}