A logical method for the synthesis of periodic trajectory in a binary dynamical system

A logic method for structural-parametric synthesis of a binary dynamical system with a given periodic trajectory is proposed. This method provides a constructive solution for the considered problem. The attraction region of such a trajectory must coincide with a given subset of the state space. An additional constraint sets the acceptable time for reaching this trajectory from its attraction region. As admissible structures for dynamical models of the synthesis, we consider the following systems: linear systems, systems with the disjunctive and conjunctive right sides. All conditions of the problem are written in the form of a quantified Boolean formula with subsequent verification of its truth using a specialized solver, which gives values of the required parameters of the dynamical model. The software implementation of the proposed method in the form of a composite service is presented. All stages of the parametric synthesis of a Boolean network based on the proposed method are demonstrated in the example of a one-step linear system.