Sequential Machines Realizable with Delay Elements Only

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Abstract
This note is concerned with the realization of sequential machines without logic, i. e., using delay elements only. The other approach to the problem deals with only the next-state behavior and tends to be rather long. A new approach is presented for not only the next-state behavior, but also for the complete behavior. Beginning with the output partitions, the predecessors are found until the process terminates with an input partition, a trivial partition, a previously found partition, or a nontrivial function of input and internal states. Whenever the latter occurs, the machine requires logic. With respect to the next-state behavior, it is first shown that a permutation machine is logic-free if and only if it is autonomous. Then since the next-state behavior of a feedback-free machine is realizable without logic, a machine is logic-free realizable if and only if M, is autonomous.

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