R70-42 Synthesis of Linear Sequential Machines with Unspecified Outputs

This paper is yet another solution for finding linear internal state assignments for the next-state behavior of a sequential machine. A state assignment is said to be linear if and only if the resulting next-state variables are linear combinations of the present-state and input variables. Consequently, the next-state behavior of a sequential machine is said to be linear if and only if there exists a one-to-one assignment which is linear. The problem of finding linear assignments has received considerable attention, probably due to their inherent mathematical structure, and hopefully to further illuminate the theory of sequential machines in general.