Bisimulations of nonlinear feedback shift registers

Abstract

This work investigates how to reduce nonlinear feedback shift registers (NFSRs) in combination with bisimulation method via semi-tensor product (STP). By considering a large-scale NFSR as a smaller-scale Boolean system utilising bisimulation relations, the computing complexity of the system can be decreased. On the one hand, the properties of the bisimulation relation between two different NFSRs are examined, while on the other hand, a necessary and sufficient condition is discovered, as well as a reduction strategy utilising bisimulation. Besides, it is talked about how NFSR properties spread throughout the reduction process. The nonsingularity, driven stability and other aspects of the original NFSR are confirmed to be preserved by the reduced Boolean system.