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G-automata, counter languages and the Chomsky hierarchy | | Murray Elder
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9 Aug 2005 | | Subject: | Group Theory MSC-class: 20F65 | math.GR | | Abstract: | We consider how the languages of $G$-automata compare with other formal language classes. We prove that if the word problem of a group $G$ is accepted by a machine in the class $mathcal M$ then the language of any $G$-automaton is in the class $mathcal M$. It follows that the so called {emph counter languages} (languages of $mathbb Z^n$-automata) are context-sensitive, and further that counter languages are indexed if and only if the word problem for $mathbb Z^n$ is indexed. | | Source: | arXiv, math.GR/0508166 | | Services: | Forum | Review | PDF | Favorites | |
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