N-decomposition and decomposition matrix for automata
Arthur T. Poe · 1973
This continues the study on generalized mutiple decomposition allowing 2-way interconnection [1]. Let NεZ+.An automaton M = is an N-automaton iff the set of states D ≤ πSi and each Si = πi (D) where πi is the projection map onto the ith component. Since the states in an N-automation are N-tuples, we may interpret M as consisting of N component automata Ml,..MN, where Mi = for each i.If (sl,..sN,t)ε D(F),then fi (si,(πsi,t))= πi(F((sl,..SN),t). We call an N-automation M = a generalized N-decomposition (GND) of M = if M realizes M. Any GND of M induces a set of N *-covers on S. A sufficient condition for a set of *-covers to give rise to a GND is established. The Properties of a GND can be represented by a matrix of relations. The diagonal entries are induced by the components and the off-diagonal entries represent the interconnections.The conditions which give rise to zero connection lines are then determined.