On the Cost of Simulating a Parallel Boolean Automata Network by a Block-Sequential One

  • Florian Bridoux
  • Pierre Guillon
  • Kévin Perrot
  • Sylvain Sené
  • Guillaume Theyssier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10185)


In this article we study the minimum number \(\kappa \) of additional automata that a Boolean automata network (BAN) associated with a given block-sequential update schedule needs in order to simulate a given BAN with a parallel update schedule. We introduce a graph that we call \({{\mathrm{\mathsf {NECC}}}}\) graph built from the BAN and the update schedule. We show the relation between \(\kappa \) and the chromatic number of the \({{\mathrm{\mathsf {NECC}}}}\) graph. Thanks to this \({{\mathrm{\mathsf {NECC}}}}\) graph, we bound \(\kappa \) in the worst case between n / 2 and \(2n/3+2\) (n being the size of the BAN simulated) and we conjecture that this number equals n / 2. We support this conjecture with two results: the clique number of a \({{\mathrm{\mathsf {NECC}}}}\) graph is always less than or equal to n / 2 and, for the subclass of bijective BANs, \(\kappa \) is always less than or equal to \(n/2+1\).


Boolean automata networks Intrinsic simulation Block-sequential update schedules 



This work has been partially supported by the project PACA APEX FRI.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Florian Bridoux
    • 1
  • Pierre Guillon
    • 2
  • Kévin Perrot
    • 1
  • Sylvain Sené
    • 1
    • 3
  • Guillaume Theyssier
    • 2
  1. 1.Université d’Aix-Marseille, CNRS, LIFMarseilleFrance
  2. 2.Université d’Aix-Marseille, CNRS, Centrale Marseille, I2MMarseilleFrance
  3. 3.Institut rhône-alpin des systèmes complexes, IXXILyonFrance

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