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Word Problem Languages for Free Inverse Monoids

Abstract : 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.
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Tara Brough. Word Problem Languages for Free Inverse Monoids. 20th International Conference on Descriptional Complexity of Formal Systems (DCFS), Jul 2018, Halifax, NS, Canada. pp.24-36, ⟨10.1007/978-3-319-94631-3_3⟩. ⟨hal-01905631⟩

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