On the Number of Attractors of Positive and Negative Boolean Automata Circuits.

Jacques Demongeot 1 Mathilde Noual 2, 3 Sylvain Sené 2, 4
1 TIMB
TIMC-IMAG - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble
4 COSMO
IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
Abstract : In line with fields of theoretical computer science and biology that study Boolean automata networks often seen as models of regulation networks, we present some results concerning the dynamics of networks whose underlying interaction graphs are circuits, that is, Boolean automata circuits. In the context of biological regulation, former studies have highlighted the importance of circuits on the asymptotic dynamical behaviour of the biological networks that contain them. Our work focuses on the number of attractors of Boolean automata circuits. We prove how to obtain formally the exact value of the total number of attractors of a circuit of arbitrary size n as well as, for every positive integer p, the number of its attractors of period p depending on whether the circuit has an even or an odd number of inhibitions. As a consequence, we obtain that both numbers depend only on the parity of the number of inhibitions and not on their distribution along the circuit.
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24th IEEE International Conference on Advanced Information Networking and Applications Workshops (WAINA 2010), Apr 2010, Perth, WA, Australia. pp.782--789, 2010, 〈10.1109/WAINA.2010.141〉
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Jacques Demongeot, Mathilde Noual, Sylvain Sené. On the Number of Attractors of Positive and Negative Boolean Automata Circuits.. 24th IEEE International Conference on Advanced Information Networking and Applications Workshops (WAINA 2010), Apr 2010, Perth, WA, Australia. pp.782--789, 2010, 〈10.1109/WAINA.2010.141〉. 〈hal-00647877〉

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