On the Linearity of Autonomous Sequential Machines

This paper presents a method of determining, from the flow table of an autonomous sequential machine, whether the machine can be realized by a linear circuit which uses the minimum possible number of secondary variables. The method is based on a class of binary partitions of states, which are used to find a minimal assignment of the secondary variables such that the next state and output functions are linear. The partitions are examined in detail and the properties necessary to produce a valid assignment are developed.