The steady state system problem is NP-hard even for monotone quadratic Boolean dynamical systems

In [2], the authors give a polynomial-time algorithm for deciding for a Boolean dynamical system in which each regulatory function is a monomial whether every limit cycle is a steady state. We show that the corresponding problem is NP-hard if the class of permissible regulatory functions contains the quadratic monotone functions xi ∨ xj and xi∧xj. We also show that the problem is NP-hard if the set of permissible regulatory functions includes all functions of the type xixj and xj + 1.