Minimal Shift-Register Realizations of Sequential Machines

This paper is concerned with the problem of mechanizing synchronous sequential machines with the least number of shift registers. An algorithm, suitable for programming on a digital computer, is developed which starts with the state table of the given machine and yields mechanizations having the least possible number of shift registers. The algorithm is based on the fact that there is a one-to-one correspondence between shift registers and certain partitions of the set of states of the machine. These partitions are called shift-register partitions (SRP's), and it is shown that every SRP can be generated from two special partitions called the column partition (π
_c
) and the row partition (π
_r
). States are grouped together in π
_c
if they have transitions into common states and are grouped together in π
_r
if they have transitions from common states.