Sequences Generated by Neuronal Automata with Memory

We st udy th e sequences generated by neuronal recurrence equat ions of th e form X n = l [~l then there is a neuronal recurrence equat ion with memory length kr that generates a sequence of period lcmlp «, . . . , Pr )1', where lem deno tes the least common multiple. As an applicat ion we show tha t , for any integer ko, there is a neuronal equa tion with memory lengt h 3k , k 2:: ko, that generates a sequence of period O(k3 ) .