Before revision:  Moreover, it appears that classical dynamical analyses of reachability and attractors have a simpler computational complexity: -- reachability can be assessed in a polynomial number of iterations (instead of being PSPACE-complete with update modes); -- attractors are hypercubes, and deciding the existence of attractors with a given upper-bounded dimension is in NP (instead of PSPACE-complete with update modes) .
After revision:  Moreover, it appears that classical dynamical analyses of reachability and attractors have a simpler computational complexity: -- reachability can be assessed in a polynomial number of iterations .