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Polynomial dynamical systems over finite fields

  • II. Algebraic Methods
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Algebraic Computing in Control

Abstract

This paper is a short introduction to the theory of Polynomial Dynamical Systems over Galois fields. These dynamical systems have been found to be a usefull tool in the study of synchronisation relations specified by a declarative style real time programming langage, the Signal language.

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References

  1. P.J. Ramadge, W.M. Wonham. Supervisory Control of a class of Discret Events Processes, SIAM J. Control and Opt., 25, 1, 1987, 206–230.

    Google Scholar 

  2. P.J. Ramadge, W.M. Wonham. Controllable Sublanguage of a Given Language, SIAM J. Control and Opt., 25, 3, 1987, 637–659.

    Google Scholar 

  3. A. Benveniste, P. Le Guernic. Hybrid Dynamical Systems theory and nonlinear dynamical systems over finite fields, Proc. of CDC 88, 209–213, Austin 7–9 Dec 1989.

    Google Scholar 

  4. A. Benveniste, B. Le Goff, P. Le Guernic. Hybrid Dynamical Systems theory and the language SIGNAL. INRIA research report No. 838, 1988.

    Google Scholar 

  5. P.J.G. Ramadge, Some tractable supervisory control problems for discrete event systems modelled by Büchi automata, IEEE-AC-34 No 1, 10–20, 1989.

    Google Scholar 

  6. B. Buchberger. Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory N.K. Bose (ed.), Multidimensional Systems Theory, 184–232, D. Reidel Publishing Company.

    Google Scholar 

  7. M. Le Borgne, A. Benveniste, P. Le Guernic. Polynomial ideal theoretic methods in Diecrete Events and Hybrid Dynamical Systems Proceeding of the 28th Conference on Decision and Control, IEEE Control Systems Society, Volume 3 of 3, 1989, 2695–2700.

    Google Scholar 

  8. A. Arnold. Systèmes de transitions finis et sémantique des processus communicants T.S.I vol 9, No 3, 1990, 193–216.

    Google Scholar 

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Gérard Jacob Françoise Lamnabhi-Lagarrigue

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© 1991 Springer-Verlag

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Borgne, M.L., Benveniste, A., Le Guernic, P. (1991). Polynomial dynamical systems over finite fields. In: Jacob, G., Lamnabhi-Lagarrigue, F. (eds) Algebraic Computing in Control. Lecture Notes in Control and Information Sciences, vol 165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006940

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  • DOI: https://doi.org/10.1007/BFb0006940

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54408-1

  • Online ISBN: 978-3-540-47603-0

  • eBook Packages: Springer Book Archive

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