The Word Problem of $\mathbb{Z}^n$ Is a Multiple Context-Free Language
نویسنده
چکیده
The word problem of a group G = Σ can be defined as the set of formal words in Σ * that represent the identity in G. When viewed as formal languages, this gives a strong connection between classes of groups and classes of formal languages. For example, Anisimov [An¯ ı71] showed that a group is finite if and only if its word problem is a regular language, and Muller and Schupp [MS83] showed that a group is virtually-free if and only if its word problem is a context-free language. Above this, not much was known, until Salvati [Sal15] showed recently that the word problem of Z 2 is multiple context-free, giving first such example. We generalize Salvati's result to show that the word problem of Z n is a multiple context-free language for any n.
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