Dynamics and Associative Mapping in Additive Systems

In this paper we present a model of Additive Automata, which is particularly useful to accomplish some specific associative tasks. For such systems and, generally, for neural nets a functional requirement is a non-ergodic evolution of net states, therefore it is useful to know some relationships between the structure of the net state space and the evolution law of the single processing element. In this way the aim of this paper is to analyze the dynamics of such systems (structure of attraction basins, cycle lenghts, number of transient states, etc….) and present a tool (well known constants of motion) to factorize the space of the net states into subspaces. Finally we give two simple laws which enable us to memorize either patterns or associations among them.