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: a) where the output is given and is to be linear, and b) where the output is either not given or may be nonlinear. The method is simple, straight-forward and in general provides a ready solution to the linearity problem.