Identification and synthesis of linear sequential machines

This paper considers the identification and synthesis of linear sequential machines from their state transition tables. Necessary and sufficient conditions for linearity are derived which form the basis of identification tests. A sufficient condition leads to a method for coding the system's state vectors in a fashion consistent with linearity but which does not entail trial and error. The coding process is analytic in nature and allows the coding of state vectors independently of the coding or linearity of the output table. Both the Moore and Mealy models are considered in deriving coding procedures for the input and output vectors.