Algorithmic properties of inverse monoids with hyperbolic and tree-like Sch\"utzenberger graphs
Group Theory
2022-11-18 v3
Abstract
We prove that the class of finitely presented inverse monoids whose Sch\"utzenberger graphs are quasi-isometric to trees has a uniformly solvable word problem, furthermore, the languages of their Sch\"utzenberger automata are context-free. On the other hand, we show that there is a finitely presented inverse monoid with hyperbolic Sch\"utzenberger graphs and an unsolvable word problem.
Keywords
Cite
@article{arxiv.1912.00950,
title = {Algorithmic properties of inverse monoids with hyperbolic and tree-like Sch\"utzenberger graphs},
author = {Robert D. Gray and Pedro V. Silva and Nóra Szakács},
journal= {arXiv preprint arXiv:1912.00950},
year = {2022}
}
Comments
Revised version with minor changes