Abstract
This paper places the work of H. Walter on classification of grammars and languages via topology in a more general framework and provides short proofs of his main results. Also, it is proved that every grammar is topologically equivalent to one in normal form, that the discrete topology can be realized on every context-free language, and that a language is finite if and only if every topology on it can be realized as one of the topologies proposed by Walter. In addition, a new and straightforward approach is provided to yield the necessary background results, on divisibility and cancellation in categories of derivations, due to D. Benson and G. Hotz.
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References
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H. Walter, Topologies on Formal Languages.Math. Systems Theory 9, 142–158 (1975).
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Nelson, E. Categorical and topological aspects of formal languages. Math. Systems Theory 13, 255–273 (1979). https://doi.org/10.1007/BF01744299
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DOI: https://doi.org/10.1007/BF01744299