Strictly connected group automata. (English) Zbl 0589.68043
To every (semi-) automaton \(S=(Q,A,F)\) where \((Q,+)\) is a group, the ”syntactic” near-ring N(S) of all state-transition functions on Q is studied. If S is ”strictly connected”, the powerful density theorems for rings and near-rings completely determine N(S). The connectedness of S is much harder to obtain if S is linear.