Complexity of Limit-Cycle Problems in Boolean Networks

Boolean networks are a general model of interacting entities, with applications to biological phenomena such as gene regulation. Attractors play central role, and the schedule entity updates is priori unknown. This article presents results on computational complexity problems related existence update schedules that some limit-cycle lengths possible or not. We first prove given network updated in parallel, knowing whether it has at least one length k \({\mathsf {NP}}\)-complete. Adding an existential quantification block-sequential does not change class problem, but following alternation brings us level above polynomial hierarchy: network, there exists no {NP^{NP}}}\)-complete.