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This paper considers the word problem for free inverse monoids of finite rank from a language theory perspective. It is shown that no free inverse monoid has context-free word problem; that the word problem of the free inverse monoid of rank $1$ is both $2$-context-free (an intersection of two context-free languages) and ET0L; that the co-word problem of the free inverse monoid of rank $1$ is context-free; and that the word problem of a free inverse monoid of rank greater than $1$ is not poly-context-free.
Motivated by the question of which completely regular semigroups have context-free word problem, we show that for certain classes of languages $mathfrak{C}$(including context-free), every completely regular semigroup that is a union of finitely many
This paper studies the classes of semigoups and monoids with context-free and deterministic context-free word problem. First, some examples are exhibited to clarify the relationship between these classes and their connection with the notions of word-
This note proves a generalisation to inverse semigroups of Anisimovs theorem that a group has regular word problem if and only if it is finite, answering a question of Stuart Margolis. The notion of word problem used is the two-tape word problem -- t
We consider the class of groups whose word problem is poly-context-free; that is, an intersection of finitely many context-free languages. We show that any group which is virtually a finitely generated subgroup of a direct product of free groups has
We prove a sufficient condition under which a semigroup admits no finite identity basis. As an application, it is shown that the identities of the Kauffman monoid $mathcal{K}_n$ are nonfinitely based for each $nge 3$. This result holds also for the c