Linearity Testing and Realization of Sequential Machines

The necessary and sufficient conditions for the linear realizability of a sequential machine are stated. The discussion considers the state transition and output functions separately and thus machines with nonlinear output function can also be tested for linearity of the state transition function. It then goes on to determine the characterizing matrices and corresponding secondary state assignment when such realization exists. The method can be applied to both permutation and nonpermutation machines.