Determining a singleton attractor of an AND/OR Boolean network in O(1.587n) time

The Boolean network (BN) is a discrete model of gene regulatory networks [5]. Each node in this network corresponds to a gene, and takes on a value of 1 or 0, meaning that the gene is or is not expressed. The value of a node at a given time instant is determined according to a regulation rule that is a Boolean function of the values of the predecessors of the node at the previous time, or their negations. The values of nodes change synchronously. We focus here on AND/OR Boolean networks, in which the regulation rule assigned to each node is restricted to be either a conjunction or a disjunction of literals. An important characteristic of any BN is the existence of an attractor, whether it is a singleton attractor, i.e. a stable state, or a cyclic attractor, i.e. a state that repeats periodically. Here the state of a network at a given time instant is the set of its node values. Unfortunately, the problem of detection of a singleton attractor (or an attractor of the shortest