On the Convergence of Boolean Automata Networks without Negative Cycles

  • Tarek Melliti
  • Damien Regnault
  • Adrien Richard
  • Sylvain Sené
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8155)

Abstract

Since the 1980’s, automata networks have been at the centre of numerous studies, from both theoretical (around the computational abilities) and applied (around the modelling power of real phenomena) standpoints. In this paper, basing ourselves on the seminal works of Robert and Thomas, we focus on a specific family of Boolean automata networks, those without negative cycles. For these networks, subjected to both asynchronous and elementary updating modes, we give new answers to well known problems (some of them having already been solved) about their convergence towards stable configurations. For the already solved ones, the proofs given are much simpler and neater than the existing ones. For the others, in any case, the proofs presented are constructive.

Keywords

Boolean automata networks cycles monotony convergence and convergence time 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Tarek Melliti
    • 1
  • Damien Regnault
    • 1
  • Adrien Richard
    • 2
  • Sylvain Sené
    • 1
    • 3
  1. 1.Laboratoire IBISC, EA4526Université d’Évry Val-d’EssonneÉvryFrance
  2. 2.Laboratoire I3SUMR7271 CNRS et Université de Nice Sophia AntipolisSophia AntipolisFrance
  3. 3.IXXIInstitut rhône-alpin des systèmes complexesLyonFrance

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