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Ultimately periodic words of rational ω-languages

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Mathematical Foundations of Programming Semantics (MFPS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 802))

Abstract

In this paper we initiate the following program: Associate sets of finite words to Büchi-recognizable sets of infinite words, and reduce algorithmic problems on Büchi automata to simpler ones on automata on finite words. We know that the set of ultimately periodic words UP(L) of a rational language of infinite words L is sufficient to characterize L, since UP(L 1)=UP(L 2) implies L 1=L 2. We can use this fact as a test, for example, of the equivalence of two given Büchi automata. The main technical result in this paper is the construction of an automaton which recognizes the set of all finite words u · $ · v which naturally represent the ultimately periodic words of the form u · 554-01 in the language of infinite words recognized by a given Büchi automaton.

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Bibliography

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Author information

Authors and Affiliations

  1. LITP, Université de Paris 7, 2,place Jussieu, 75251, Paris Cedex 05, France

    Hugues Calbrix & Maurice Nivat

  2. Digital PRL, 85, avenue Victor Hugo, 92563, Rueil-Malmaison, France

    Andreas Podelski

Authors
  1. Hugues Calbrix
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  2. Maurice Nivat
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  3. Andreas Podelski
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Editor information

Stephen Brookes Michael Main Austin Melton Michael Mislove David Schmidt

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© 1994 Springer-Verlag Berlin Heidelberg

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Calbrix, H., Nivat, M., Podelski, A. (1994). Ultimately periodic words of rational ω-languages. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds) Mathematical Foundations of Programming Semantics. MFPS 1993. Lecture Notes in Computer Science, vol 802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58027-1_27

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  • DOI: https://doi.org/10.1007/3-540-58027-1_27

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58027-0

  • Online ISBN: 978-3-540-48419-6

  • eBook Packages: Springer Book Archive

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