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Topologies on formal languages

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Abstract

S. Y. Kuroda has shown that it is possible to attack problems concerning syntactic analysis and translation by means of topological concepts and methods. He presented a way to introduce topologies on context-free languages via the generating grammar, by considering all extensions of nonterminal derivations.

We extend Kuroda's concept to the general case of languages and study continuous mappings, compactness and topological connectness. The main tool is an appropriate definition of structural equivalence of grammars and languages, presented with the help of topologies and homeomorphisms. We derive theorems on the topological equivalence of grammars and languages.

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Authors and Affiliations

  1. Fachbereich Informatik, Technische Hochschule Darmstadt, D 61, Darmstadt, West Germany

    Herman Walter

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  1. Herman Walter
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Walter, H. Topologies on formal languages. Math. Systems Theory 9, 142–158 (1975). https://doi.org/10.1007/BF01704017

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  • DOI: https://doi.org/10.1007/BF01704017

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