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Counting with rational functions

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Automata, Languages and Programming (ICALP 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 226))

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Abstract

Rational functions of a free monoid A* into the free cyclic monoid t* generated by a unique element t, can be viewed as assigning an integer to every word u∈A*. We investigate those functions which count occurrences of some fixed (and special) subsets \(X \subseteq A^ *\) in all words of A* and show that they can be characterized in terms of "bounded variation", a notion which is close to continuity of functions.

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Author information

Authors and Affiliations

  1. Faculté des Sciences, Université de ROUEN, B.P. 67, 76130, Mont-Saint-Aignan

    C. Choffrut

  2. U.E.R. de Mathématiques et d'Informatique, Université Paris 7, 2, place Jussieu, Tout 55-56, ler étage, 75251, Parix Cedex 05

    M. P. Schutzenberger

Authors
  1. C. Choffrut
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  2. M. P. Schutzenberger
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Editor information

Laurent Kott

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© 1986 Springer-Verlag Berlin Heidelberg

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Choffrut, C., Schutzenberger, M.P. (1986). Counting with rational functions. In: Kott, L. (eds) Automata, Languages and Programming. ICALP 1986. Lecture Notes in Computer Science, vol 226. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16761-7_57

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  • DOI: https://doi.org/10.1007/3-540-16761-7_57

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16761-7

  • Online ISBN: 978-3-540-39859-2

  • eBook Packages: Springer Book Archive

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