Accessibility and Connectness in Automata Network with General Updating Rules

Abstract

We propose a method for analysis and control of dynamical behavior of automata network in the form of block-sequential iteration with delays, i.e. with a memory of some depth. The properties of accessibility and connectness are considered. We reduce automata model complexity by means of model transformations in a class of homomorphisms. These functions play an important role in our theory and act as Lyapunov functions in stability theory. In terms of these functions criteria of existence of the above mentioned properties are formulated.