The transformation between Galois type and Fibonacci type of nonlinear feedback shift registers (NFSRs) is investigated. First, the algebraic forms of Galois NFSRs and Fibonacci NFSRs are proposed respectively by viewing the NFSR as a Boolean network. Then, the observability of NFSRs is defined and the observability matrix is constructed, based on which, some necessary and sufficient conditions for the transformation between an n-stage Galois NFSR and a Fibonacci NFSR with the same stage or stage less than n are obtained. Finally, two examples are provided to depict the theoretical results.

中文翻译：

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Galois NFSRs 和 Fibonacci NFSRs 之间的等价变换

研究了伽罗瓦型和斐波那契型非线性反馈移位寄存器（NFSR）之间的转换。首先，通过将 NFSR 视为布尔网络，分别提出了 Galois NFSR 和 Fibonacci NFSR 的代数形式。然后，定义了NFSRs的可观测性，构造了可观测性矩阵，在此基础上得到了n阶Galois NFSR与同阶或小于n阶的Fibonacci NFSR之间转换的一些充要条件。最后，提供了两个例子来描述理论结果。