Synchronization of Boolean Dynamical Systems: A Spectral Characterization

  • Jérémy Parriaux
  • Philippe Guillot
  • Gilles Millérioux
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6338)


In this paper a spectral characterization of the synchronization property of Boolean dynamical systems is provided. Conditions on the spectrum of the next-state function are derived for two systems coupled in a unidirectional way - also called master-slave configuration - to guarantee self-synchronization. Two kinds of self-synchronization are discussed: the statistical one and the finite one. Next, some conditions are stated for a specific input sequence to allow the system to be self-synchronizing. Some of the results are based on the notion of influence of variables, a notion that is extended to vectorial Boolean functions for the purpose of the paper. A potential application to cryptography is finally given.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jérémy Parriaux
    • 1
  • Philippe Guillot
    • 2
  • Gilles Millérioux
    • 1
  1. 1.Research Center for Automatic Control of Nancy (CRAN UMR 7039)Nancy University, CNRSFrance
  2. 2.Laboratoire Analyse, Géométrie et Applications (LAGA UMR 7539)Université Paris 8France

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