Issue No. 08 - August (1971 vol. 20)

ISSN: 0018-9340

pp: 929-933

ABSTRACT

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.

INDEX TERMS

Autonomous machines, periodic representations, reducibility, sequential machines, serial and parallel decomposition, state-splitting problem, T-partitionable equivalents.

CITATION

J.W. Grzymala-Busse, "On the Decomposition of Periodic Representations of Sequential Machines",

*IEEE Transactions on Computers*, vol. 20, no. , pp. 929-933, August 1971, doi:10.1109/T-C.1971.223374