Secondary State Assignment for Sequential Machines

One of the most important and complicated problems in the synthesis of a sequential machine described by a state diagram or table is the assignment of the states of the secondary variables to the states of the machine. The secondary assignment for a given machine varies in accordance with the requirements of the design. It has already been shown that the partition with the substitution property and the partition pairs are of great significance in the secondary assignment. However, only few machines possess these properties, and hence, a more general method is needed. This paper presents a method of obtaining for any given machine M an equivalent machine M' which has a partition with the substitution property or partition pairs and therefore can be decomposed into two or more submachines connected in cascade or possibly in parallel. It is also shown that for machine M' we can find an assignment with self-dependent subsets. The method is shown to be general for any completely or incompletely specified sequential machine.