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arXiv · 2205.08854

On the rational subsets of the monogenic free inverse monoid

Pedro V. Silva
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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 $\mathcal{J}$-above monoid is decidable, covering the case of free inverse monoids.

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Pedro V. Silva. 2022-05-18. On the rational subsets of the monogenic free inverse monoid. https://arxiv.org/abs/2205.08854

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