Abstract
Some binary sequences generated by feedback shift registers have many important applications, and their research has also received more and more attention. This paper research the monotonicity and local stability of Grain-like cascade feedback shift registers (FSRs) systems. Grain-like cascade FSRs differ from general feedback shift registers in that they consist of two parts, a linear feedback shift register (LFSR) and a nonlinear feedback shift register (NFSR), so the study of Grain-like cascade FSRs is more complicated. A method based on semi-tensor product (STP) is used to study the monotonicity and local stability of Grain-like cascade FSRs, we get necessary conditions about the monotonicity, and sufficient and necessary about local stability of Grain-like cascade FSRs.
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