On Shift-Register Realizations of Sequential Machines and Finite-State Universal Sequential Machines

Abstract—It is shown that there exist finite-state universal sequential machines which are also feedback-shift-register realizable. This proves from another point of view the recently proved fact that any arbitrary sequential machine can be realized with two shift registers: one which is not always binary, stores the input, and has no feedback; and the other which is always binary, is driven from the first shift register, and has feedback. In addition, it is proved that the communication between the two shift registers can be reduced to a single binary line.