AND-OR networks are Boolean networks where each coordinate function is either the
AND or OR logical operator. We study the number of fixed points of these Boolean
networks in the case that they have a wiring diagram with chain topology. We find
closed formulas for subclasses of these networks and recursive formulas in the general
case. Our results allow for an effective computation of the number of fixed points in
the case that the topology of the Boolean network is an open chain (finite or infinite)
or a closed chain. We further explore how our approach could be used in “fractal”
chains.
