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- W3106811412 abstract "A monoid is compressible if it admits a presentation in which all words in the defining relations begin and end with some specified word. Associated to any compressible monoid $M$ is a compressed left monoid $L(M)$. We study the language-theoretic properties of the word problem, in the sense of Duncan & Gilman, of compressible monoids. We prove that if $mathcal{C}$ is a superAFL, then $M$ has word problem in $mathcal{C}$ if and only if $L(M)$ has word problem in $mathcal{C}$. In particular, this applies when $mathcal{C}$ is the class of context-free languages. As a corollary, we deduce that if $L(M)$ has context-free word problem, then the rational subset membership problem for $M$ is decidable. We also consider subspecial monoids, which are the one-relation monoids that can be compressed to special monoids. In this case we extend the above results, and show that a subspecial monoid has context-free word problem if and only if all its maximal subgroups are virtually free. This gives a generalisation of the Muller-Schupp theorem to subspecial monoids." @default.
- W3106811412 created "2020-12-07" @default.
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- W3106811412 date "2020-12-02" @default.
- W3106811412 modified "2023-09-27" @default.
- W3106811412 title "On the Word Problem for Compressible Monoids" @default.
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