The Behavior and Learning of a Deterministic Neural Net
Eduardo R. Caianiello
Anna Esposito
Maria Marinaro
Dipartimento di Fisica Teorica,
Università di Salerno,
Via S. Allende 84081 Baronissi, Salerno, Italy
Roberto Tagliaferri
Dipartimento di Informatica e Applicazioni,
Università di Salerno,
Via S. Allende 84081 Baronissi, Salerno, Italy
Abstract
This paper is devoted to the study of the behavior of a specific but large class of linear boolean nets. The class is obtained by fixing the synaptic matrix 
, which connects the 
neurons, in such a way that a specific set of patterns evolves linearly. Our main result consists of the establishment of connections between the evolution of the patterns of the specific set and the evolution of the complete set of 
states. In particular, the stable states of the network and their attraction basins can be obtained from knowledge of the stable states of the specific set. In addition, we give a rule to store these states, and to obtain an Associative Memory in computational time (polynomial in ).
