The object of this paper is to study the realization of a sequential machine from several smaller machines. The basic tools in this investigation are the partitions with the substitution property and the partition pairs. It is shown that to every (loop-free) realization of a sequential machine from n smaller machines corresponds a set of n partitions with the substitution property whose product is the zero partition. Conversely, it is shown that to every such set of n partitions corresponds a realization of the given sequential machine from n smaller machines. The natural ordering of these partitions is reflected in the information flow between the corresponding component machines and the algebraic operations defined between these partitions corresponding to the realization, govern the modifications of this realization. Finally, it is shown how the amount of information flowing between the component machines in a realization can be studied by means of partition pairs.
