On the rational subsets of the monogenic free inverse monoid

DOI10.1016/J.JALGEBRA.2022.12.006arXiv2205.08854MaRDI QIDQ6399470

Pedro V. Silva

Publication date: 18 May 2022

Abstract: We prove that the equality problem is decidable for rational subsets of the monogenic free inverse monoid $F$. It is also decidable whether or not a rational subset of $F$ is recognizable. We prove that a submonoid of $F$ is rational if and only if it is finitely generated. We also prove that the membership problem for rational subsets of a finite $mathcalJ$-above monoid is decidable, covering the case of free inverse monoids.

Mathematics Subject Classification ID

Formal languages and automata (68Q45) Free semigroups, generators and relations, word problems (20M05) Semigroups in automata theory, linguistics, etc. (20M35) Inverse semigroups (20M18)

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