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On the Decomposition of Periodic Representations of Sequential Machines
August 1971 (vol. 20 no. 8)
pp. 929-933
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. 8, pp. 929-933, Aug. 1971, doi:10.1109/T-C.1971.223374
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