For every fixed k ≥ 2 the cyclic attractor detection problem is NP-complete precisely when the local Boolean function class contains majority-like self-dual rules or mixed conjunctive-disjunctive monotone families, and polynomial-time solvable in all other Post classes.
Positive Feedback Loops and Multistationarity
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Cyclic Attractor Detection in Boolean Network Dynamics under Local Logical Constraints
For every fixed k ≥ 2 the cyclic attractor detection problem is NP-complete precisely when the local Boolean function class contains majority-like self-dual rules or mixed conjunctive-disjunctive monotone families, and polynomial-time solvable in all other Post classes.