Maximum number of fixed points in AND–OR–NOT networks

Abstract : We are interested in the number of fixed points in AND-OR-NOT networks, i.e. Boolean networks in which the update function of each component is either a conjunction or a disjunction of positive or negative literals. As main result, we prove that the maximum number of fixed points in a loop-less connected AND-OR-NOT network with n components is at most the maximum number of maximal independent sets in a loop-less connected graph with n vertices, a quantity already known.
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J Aracena, Adrien Richard, L Salinas. Maximum number of fixed points in AND–OR–NOT networks. Journal of Computer and System Sciences, Elsevier, 2014, ⟨10.1016/j.jcss.2014.04.025⟩. ⟨hal-01298835⟩

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