On the Decomposition of Periodic Representations of Sequential Machines

In this note a sequential machine decomposition implied by the fact that this machine possesses a nontrivial periodic representation is discussed. If it is fulfilled, then for the state behavior of such a sequential machine there exists a nontrivial serial decomposition into two machines, where one of them is autonomous. Moreover, if for a sequential machine there exists a reducible periodic representation, then for the state behavior of this sequential machine there exists a nontrivial parallel decomposition into two machines such that one of them is autonomous. These results permit us to discuss the state-splitting problem with the aid of the T-partitionable equivalency.