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.
Keywords
T. Brough—The author was supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through an FCT post-doctoral fellowship (SFRH/BPD/121469/2016) and the projects UID/Multi/04621/2013 (CEMAT-CIÊNCIAS) and UID/MAT/00297/2013 (Centro de Matemática e Aplicações).
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- 1.
The language \(L^{(2,k)}\) in the referenced result is not precisely \(W_k\), but the associated set of integer tuples differs from that associated to \(W_k\) only by a constant (arising from the symbol \(\#\)), which does not affect stratification properties and therefore does not affect the property of not being \((k-1)\)-\(\mathcal {CF}\).
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Brough, T. (2018). Word Problem Languages for Free Inverse Monoids. In: Konstantinidis, S., Pighizzini, G. (eds) Descriptional Complexity of Formal Systems. DCFS 2018. Lecture Notes in Computer Science(), vol 10952. Springer, Cham. https://doi.org/10.1007/978-3-319-94631-3_3
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