Istituto di Scienza e Tecnologie dell'Informazione     
Gerace G. B., Gestri G. State assignments for reducing the number of delay elements in sequential machines. In: Information and Control, vol. 10 (3) pp. 223 - 256. Academic Press, 1967.
It has been previously shown that internal state assignments can be used for reducing the number of combinational elements in sequential machines. In this paper it is shown that state assignments can also be employed for reducing the number of delay elements in such machines. This will be done for a "realization with PFM circuits," which is a particular pulse-input fundamental-mode realization of a sequential machine. It will be shown that the existence of assignments which reduce the number of delay elements in machines realized with PFM circuits is closely related to the existence of a "NNP pair" of partitions, that is, a partition with nonnegation property with respect to a partition with substitution property (Hartrnanis). A general method will be given which selects the assignments which minimize the number of delay elements in realizations with PFM circuits, but it will be outlined that this method can also be used for reclucing the number of delay elements which are present in the feedback paths of synchronous machines.

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