On the convergence of Boolean automata networks without negative cycles

Tarek Melliti (1) , Damien Regnault (2) , Adrien Richard (2) , Sylvain Sené (3, 1)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe BIOINFO
3 IXXI - Institut Rhône-Alpin des systèmes complexes

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 speci c 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 con gurations. 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.

Mots clés: Boolean automata networks; cycles; monotony; convergence and convergence time

Domaines: Complexité [cs.CC]; Mathématique discrète [cs.DM]

Tarek Melliti, Damien Regnault, Adrien Richard, Sylvain Sené. On the convergence of Boolean automata networks without negative cycles. 19th International Workshop on Cellular Automata and Discrete Complex Systems (AUTOMATA 2013), Sep 2013, Gießen, Germany. pp.124--138, ⟨10.1007/978-3-642-40867-0_9⟩. ⟨hal-00832885⟩