Asynchronous Simulation of Boolean Networks by Monotone Boolean Networks

  • Tarek Melliti
  • Damien Regnault
  • Adrien Richard
  • Sylvain Sené
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9863)

Abstract

We prove that the fully asynchronous dynamics of a Boolean network \(f:\{0,1\}^n\rightarrow \{0,1\}^n\) without negative loop can be simulated, in a very specific way, by a monotone Boolean network with 2n components. We then use this result to prove that, for every even n, there exists a monotone Boolean network \(f:\{0,1\}^n\rightarrow \{0,1\}^n\), an initial configuration x and a fixed point y of f such that: (i) y can be reached from x with a fully asynchronous updating strategy, and (ii) all such strategies contains at least \(2^{\frac{n}{2}}\) updates. This contrasts with the following known property: if \(f:\{0,1\}^n\rightarrow \{0,1\}^n\) is monotone, then, for every initial configuration x, there exists a fixed point y such that y can be reached from x with a fully asynchronous strategy that contains at most n updates.

Keywords

Boolean networks Monotone networks Asynchronous updates 

Notes

Acknowledgment

This work has been partially supported by the project PACA APEX FRI. We wish also to thank Pierre-Etienne Meunier, Maximilien Gadouleau and an anonymous reviewer for stimulating discussions and interesting remarks.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Tarek Melliti
    • 1
  • Damien Regnault
    • 1
  • Adrien Richard
    • 2
  • Sylvain Sené
    • 3
  1. 1.Université d’Évry Val-d’Essonne, CNRS, IBISC EA 4526ÉvryFrance
  2. 2.Université de Nice Sophia Antipolis, CNRS, I3S UMR 7271Sophia-AntipolisFrance
  3. 3.Aix-Marseille Université, CNRS, LIF UMR 7279MarseilleFrance

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