Automata dynamics preserved under homomorphism: connectness, reachability, optimality

We propose a general approach to analysis and control of dynamical behavior of an automata network. The properties of connectness, reachability and optimality under phase constraints and/or persistently acting perturbations are considered. We reduce automata model complexity by means of model transformations in a class of logical functions. These functions play an important part in our theory and act as Lyapunov functions in stability theory or homomorphisms in automata theory. In terms of these logical functions criteria of existence of above mentioned properties are formulated. Constructive algorithms of generating the logical functions satisfying the criteria as well as examples of their application are described