Reduction of Output Dependency in Sequential Machines

The realization of the output circuit is a topic which has been neglected in current publications in spite of the indisputable importance of the subject. In recent papers dealing with the problem of secondary assignment [1]-[3], [5], the main consideration was given to the transitions between the states and the realization of the circuits that control the secondary variables. In assigning the states of the secondary variables to the blocks of the partitions with substitution property or to the blocks of the partition pairs, we have a considerable amount of freedom. In the present paper it is shown how this freedom is used in order to obtain simpler Output circuits with reduced dependencies. The chief tools in this discussion are the partitions with substitution property in conjunction with the output-consistent partitions. Further it is shown how a simpler output circuit can be obtained by recognizing ``partially independent'' subsets in the output table and by using this property in order to achieve an assignment with reduced dependencies. The concept of partially independent subsets is seen to apply to machines which do not possess any partitions with substitution property or partition pairs and is used as a tool for obtaining simpler secondary assignments as well as simpler output circuits.