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Context-free sets of infinite words

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Theoretical Computer Science 4th GI Conference

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 67))

Abstract

In this paper we give some new results about context-free sets of infinite words. The presentation will be a generalization of McNaughton's approach in [7], where he analyzed regular sets of infinite words. However, our extension to the regular case is not straightforward and thus distinguishes from the approach given in [4].

Some of the results given below originate from two papers by Nivat [9,10], others are unpublished supplementary results due to Nivat and Boasson.

We recall from [9] that to each context-free grammar G one can associate an operator Ĝ, which has a unique fixed point over finite words and a greatest fixed point over finite and infinite words, each of them being the vector of languages generated by the non-terminals of G.

We then show that any context-free set of infinite words can be obtained by a substitution of some context-free languages into a regular set of infinite words.

In the sequel the notions of adherence and center of context-free languages are introduced and analyzed to establish a link between the infinite words and the language generated by a grammar.

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References

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Authors

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K. Weihrauch

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© 1979 Springer-Verlag Berlin Heidelberg

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Boasson, L. (1979). Context-free sets of infinite words. In: Weihrauch, K. (eds) Theoretical Computer Science 4th GI Conference. Lecture Notes in Computer Science, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09118-1_1

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  • DOI: https://doi.org/10.1007/3-540-09118-1_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09118-9

  • Online ISBN: 978-3-540-35517-5

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