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Bilinear Functions and Trees over the (max, +) Semiring

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Mathematical Foundations of Computer Science 2000 (MFCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1893))

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Abstract

We consider the iterates of bilinear functions over the semiring (max,+). Equivalently, our object of study can be viewed as recognizable tree series over the semiring (max,+). In this semiring, a fundamental result associates the asymptotic behaviour of the iterates of a linear function with the maximal average weight of the circuits in a graph naturally associated with the function. Here we provide an analog for the ‘iterates’ of bilinear functions. We also give a triple recognizing the formal power series of the worst case behaviour.

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Author information

Authors and Affiliations

  1. LIAFA Université Paris VII, Case 7014 2 place Jussieu, 75251, Paris Cedex 05, France

    Sabrina Mantaci & Jean Mairesse

  2. Department of Mathematical Engineering, CESAME - University of Louvain, Avenue Georges Lemaitre, 4, B-1348, Louvain-la-Neuve, Belgium

    Vincent D. Blondel

Authors
  1. Sabrina Mantaci
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  2. Vincent D. Blondel
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  3. Jean Mairesse
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, 8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Department of Computer Sciene, Comenius University, 84248, Bratislava, Slovakia

    Branislav Rovan

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© 2000 Springer-Verlag Berlin Heidelberg

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Mantaci, S., Blondel, V.D., Mairesse, J. (2000). Bilinear Functions and Trees over the (max, +) Semiring. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_50

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  • DOI: https://doi.org/10.1007/3-540-44612-5_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67901-1

  • Online ISBN: 978-3-540-44612-5

  • eBook Packages: Springer Book Archive

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