Readily Programmable Procedures for the Analysis of Nonlinear Feedback Shift Registers

Two vector operators θ and γ are introduced. The next-state operator θ allows one to calculate the successors of a set of states {G} from a binary nonlinear feedback shift register. The past-state operator γ allows one to calculate the predecessors of a set of states {G}. Both of these operators, which can be easily programmed on a digital computer, can be used to analyze autonomous and nonautonomous feedback shift registers. Analysis procedures using these operators are given for determining the cycle set of an arbitrary nonlinear FSR, for deciding if the state diagrams of the FSR are connected or strongly connected, and also for determining if the FSR is controllable.