Issue No.08 - August (1971 vol.20)
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.
Autonomous machines, periodic representations, reducibility, sequential machines, serial and parallel decomposition, state-splitting problem, T-partitionable equivalents.
J.W. Grzymala-Busse, "On the Decomposition of Periodic Representations of Sequential Machines", IEEE Transactions on Computers, vol.20, no. 8, pp. 929-933, August 1971, doi:10.1109/T-C.1971.223374