On the Linearity of Sequential Machines

This paper presents a method for determining, from the flow table of a sequential machine, whether the machine is linearly realizable using the minimum number of unit delay elements. The method is an extension of a previously presented method for autonomous machines. A linearity algorithm is presented for each of two cases: 1) where the output is given and is to be linear, and 2) where the output is either not given or may be nonlinear. The method is simple, straightforward, and, in general, provides a ready solution to the linearity problem.