Sequential Machines Realizable with Delay Elements Only

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.