Combinatorics of Boolean automata circuits dynamics

Abstract : In line with fields of theoretical computer science and biology that study Boolean automata networks to model regulation networks, we present some results concerning the dynamics of networks whose underlying structures are oriented cycles, 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 whose elements are updated in parallel. In particular, we give 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. We also relate the counting of attractors of Boolean automata circuits to other known combinatorial problems and give intuition about how circuits interact by studying their dynamics when they intersect one another in one point.
Type de document :
Article dans une revue
Discrete Applied Mathematics, Elsevier, 2012, 160 (4-5), pp.398--415. 〈10.1016/j.dam.2011.11.005〉
Liste complète des métadonnées

Littérature citée [40 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00666297
Contributeur : Frédéric Davesne <>
Soumis le : mardi 11 février 2014 - 12:49:56
Dernière modification le : jeudi 12 juillet 2018 - 01:04:49
Document(s) archivé(s) le : lundi 12 mai 2014 - 11:16:31

Fichier

dns12.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Jacques Demongeot, Mathilde Noual, Sylvain Sené. Combinatorics of Boolean automata circuits dynamics. Discrete Applied Mathematics, Elsevier, 2012, 160 (4-5), pp.398--415. 〈10.1016/j.dam.2011.11.005〉. 〈hal-00666297〉

Partager

Métriques

Consultations de la notice

685

Téléchargements de fichiers

132