Fixed points in generalized parallel and sequential dynamical systems induced by a minterm or maxterm Boolean functions

In this paper, we study the classical problems associated with fixed points in generalized parallel and sequential dynamical systems which are induced by a minterm or a maxterm Boolean function. In particular, we give a characterization of such fixed points which allows us to solve the fixed-point existence problem. Furthermore, we provide a method for counting the exact number of fixed points in such systems by means of a special kind of dominating sets. We demonstrate the main results for the case of generalized parallel dynamical systems induced by a minterm, what assure the same results in the case induced by maxterm thanks to the duality principle. In this context, the results are also valid for the sequential case, since the fixed points of any sequential system are the same of its parallel counterpart. These results generalize those given for parallel dynamical systems induced by such Boolean functions and also for normal AND-NOT networks (resp. OR-NOT networks) which are a particular case of generalized parallel dynamical systems induced by the minterm NOR (resp. maxterm NAND).